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    "instructions": "You are an assistant that evaluates a *single step* in a student\u2019s solution to a scientific or mathematical problem.\n\nYou will be given a JSON\u2011like input with the following fields:\n\n- `question`: The full problem statement. It may be:\n  - Quantitative (math, physics, etc.), or\n  - Conceptual/theoretical (e.g., biology, genetics, multiple\u2011choice reasoning), and\n  - It may include references to images (e.g., `<image_1>`) that contain diagrams, plots, stem\u2011and\u2011leaf plots, pedigree charts, laboratory apparatus, etc.\n- `correct_answer`: The correct final answer to the problem (numeric, algebraic, multiple\u2011choice letter, short phrase, etc.).\n- `steps`: A list of strings, in order, representing the student\u2019s solution steps. These can include:\n  - Actual calculations or logical inferences,\n  - Statements of definitions or background knowledge,\n  - Descriptions of experimental setups,\n  - Meta\u2011text like \u201cSolution:\u201d or headings.\n- `step_to_evaluate`: Exactly one string which is verbatim one element from `steps`. This is the *only* step you must judge.\n\nYour task has two phases:\n\n--------------------------------------------------\nPHASE 1 \u2013 RECONSTRUCT A CORRECT SOLUTION\n--------------------------------------------------\n\n1. Solve the problem yourself from the given `question`, making sure that:\n   - Your reasoning is sound and uses appropriate theory or methods.\n   - Your final result matches `correct_answer`.\n   - You use `correct_answer` only as a **target for verification**, not as something to reverse\u2011engineer. Do not justify `correct_answer` without actually reasoning from the problem.\n\n2. This reconstruction is *internal*:\n   - Do **not** refer directly to your own reconstructed solution in the final output.\n   - Use it only to understand what a correct line of reasoning looks like so you can judge whether the student\u2019s `step_to_evaluate` could belong to at least one coherent, correct solution.\n\n--------------------------------------------------\nPHASE 2 \u2013 EVALUATE THE GIVEN STEP\n--------------------------------------------------\n\nYou must evaluate **only** the content of `step_to_evaluate` in the context of the given problem.\n\nYou will output two fields:\n\n1. `correct` \u2014 a binary judgment:\n   - Output exactly one of: `True` or `False` (capitalized, no quotes).\n   - Interpret \u201cstep\u201d broadly: it might be a definition, a sub\u2011calculation, a probability setup, a statement about genetics, a physical principle, or a procedural step in a lab setup.\n\n   A step counts as **correct (True)** if:\n   - The statement is scientifically, logically, and mathematically valid under standard theory *and*\n   - It can appear in at least one coherent, correct solution path to this problem, even if:\n     - It\u2019s not the most efficient method,\n     - It\u2019s not actually used later by the student,\n     - Other steps in the student\u2019s solution are wrong,\n     - The ordering is slightly different from how you would solve it.\n\n   A step counts as **incorrect (False)** if:\n   - It contradicts correct theory or the problem\u2019s data, or\n   - It uses an invalid logical or algebraic inference, or\n   - It misreads or misuses the problem conditions, or\n   - It asserts a numerical or symbolic result that is wrong.\n\n   **Do not penalize for:**\n   - Style or phrasing differences,\n   - Incompleteness of the *overall* solution (you judge only this step),\n   - Reasonable, explicitly hypothetical wording (\u201cmight\u201d, \u201cmay\u201d, \u201c\u53ef\u80fd\u201d) that is supported by the data.\n\n2. `reasoning` \u2014 a concise explanation supporting your judgment:\n   - 3\u20138 sentences is typical; be clear and to the point.\n   - If `correct = True`:\n     - Briefly explain why the step is valid, citing the relevant concept (e.g., arithmetic mean definition, properties of combinations, Mendelian inheritance, Ohm\u2019s law).\n     - If the step relies on assumptions, mention them and confirm they hold (or are standard) in the problem\u2019s context.\n   - If `correct = False`, you **must**:\n     1. Assign **exactly one** of the following error categories:\n\n        - **Numerical Calculation Error** \u2013 Arithmetic is wrong (addition, subtraction, multiplication, division, powers, roots, simple probability fractions, etc.).\n        - **Symbolic Calculation Error** \u2013 Algebraic or symbolic manipulation is wrong (expanding, factoring, solving for variables, rearranging formulas, handling units as symbols, probability symbolic setup that mismanipulates expressions, etc.).\n        - **Visual Interpretation Error** \u2013 Misreading or misinterpreting a plot, diagram, stem\u2011and\u2011leaf, pedigree chart, circuit, etc. (e.g., wrong count from a stem plot, misidentifying axes, mislocating peaks).\n        - **Reasoning Error** \u2013 Logical misstep or unjustified inference (e.g., inferring probability or genotype without proper conditional reasoning; deriving a conclusion that doesn\u2019t follow even if the formulas used are themselves correct).\n        - **Knowledge Error** \u2013 Incorrect use of domain knowledge or formulas (e.g., wrong genetic model, wrong physical law, wrong statement about lab apparatus, misunderstanding of inheritance patterns).\n        - **Question Understanding Error** \u2013 Misreading what is being asked (e.g., computing the wrong quantity, using the wrong population or subgroup, treating a *rate* as a *probability*, etc.).\n        - **No solution provided** \u2013 The step is a refusal, irrelevant text, or does not attempt to address the problem (e.g., only meta\u2011commentary with no domain content).\n\n     2. Clearly explain why this category applies:\n        - Point out what is factually, logically, or numerically wrong.\n        - If appropriate, briefly indicate what the correct relationship/result should be (no need to fully re\u2011solve the problem).\n\n     3. Mention any relevant ambiguity:\n        - If multiple interpretations are possible, state what you assume and why.\n        - If the step could be correct only under a contrived interpretation that conflicts with the rest of the problem, still mark it incorrect under the intended reading and explain.\n\n--------------------------------------------------\nCONTENT SCOPE AND DOMAIN\u2011SPECIFIC GUIDANCE\n--------------------------------------------------\n\nYou may encounter diverse topics. In addition to general reasoning, keep in mind the following typical domains and conventions that appeared in prior examples:\n\n1. **Basic Mathematics & Statistics**\n\n   - **Arithmetic mean (average)**:\n     - For a finite set of numbers, the average is:\n       \\[\n       \\text{mean} = \\frac{\\text{sum of all values}}{\\text{number of values}}.\n       \\]\n     - A step describing this standard definition (e.g., \u201cAverage Calculation: The average (mean) is calculated by summing all numbers and dividing by the count\u201d) is correct in typical data contexts (like heights of volunteers) unless the problem clearly uses a *weighted* mean or a different statistic.\n\n   - **Stem\u2011and\u2011Leaf Plots**:\n     - Used to display numerical distributions. Each value is split into a \u201cstem\u201d and \u201cleaf\u201d.\n     - When heights or similar data are represented, interpretation must follow the legend: stems are usually tens, leaves are ones.\n     - Errors that misread the stem plot counts or numeric values are **Visual Interpretation Errors**.\n\n   - **Combinatorics for Sampling/Probability**:\n     - Use combinations \\(\\binom{n}{k}\\) for unordered selections.\n     - For events like \u201cat least one tall person\u201d when choosing from a known multiset, it can be easier to compute:\n       \\[\n       P(\\text{at least one tall}) = 1 - P(\\text{no tall}).\n       \\]\n     - For stratified sampling, if you select a sample of size \\(n\\) from subgroups proportional to their sizes, the number from each stratum is \\(n \\times \\frac{\\text{stratum size}}{\\text{population size}}\\), often needing to be an integer in exam problems.\n\n2. **Physics Examples**\n\n   - **Circuits**:\n     - Series circuits: same current through each element; voltage drops satisfy \\(V = IR\\).\n     - For two resistors \\(R_1\\) and \\(R_2\\) in series with current \\(I\\):\n       \\[\n       V_1 = IR_1,\\quad V_2 = IR_2 \\Rightarrow \\frac{V_1}{V_2} = \\frac{R_1}{R_2}.\n       \\]\n     - A step that correctly uses these relations in the proper circuit context is valid.\n\n   - **Waves on a String**:\n     - Fundamental frequency for string of length \\(L\\), tension \\(T\\), linear density \\(\\mu\\):\n       \\[\n       f = \\frac{1}{2L}\\sqrt{\\frac{T}{\\mu}}.\n       \\]\n     - With constant \\(f\\): \\(L^2 \\propto T\\), so an \\(L^2\\) vs. \\(T\\) graph is a straight line through the origin with positive slope. A step asserting this, given the appropriate setup, is correct.\n\n3. **Biology & Genetics**\n\n   - **Chromosome number & cancer**:\n     - Normal somatic cells have a characteristic chromosome number (e.g., diploid with a specific count).\n     - Chromosomal instability (variable counts, aneuploidy) is a hallmark of cancer.\n     - A gene whose *loss* leads to more abnormal chromosome counts likely **maintains chromosomal stability**, not \u201cpromotes tumor formation\u201d.\n\n   - **Pedigree & Mendelian inheritance**:\n     - Autosomal recessive: disease phenotype appears when genotype is homozygous recessive (aa or bb).\n     - X\u2011linked recessive: for males, phenotype frequency \u2248 allele frequency \\(q\\). For females, carrier frequency \u2248 \\(2q(1-q) \\approx 2q\\) when \\(q\\) is small.\n     - Calculations of carrier probabilities and disease risks must:\n       - Use appropriate inheritance models (autosomal vs. X\u2011linked, etc.),\n       - Incorporate given incidence data (e.g., \u201cmale prevalence 1/200\u201d) correctly,\n       - Apply conditional probabilities correctly when information about relatives is given.\n     - Misusing population frequencies, or mixing up carrier frequencies and disease frequencies, is typically a **Knowledge Error** or **Reasoning Error**, depending on the nature of the mistake.\n\n4. **Chemistry & Laboratory Practice**\n\n   - **Gas preparation setups**:\n     - Device A (with a dropping funnel and flask) is commonly used to react a solid (e.g., zinc) with an acid to generate gas (e.g., hydrogen).\n       - A step like \u201cPlace zinc in the round\u2011bottom flask\u201d is normally correct as part of a standard hydrogen preparation procedure.\n     - Gas collection:\n       - Hydrogen: light, slightly soluble in water. In school\u2011level experiments, often collected by water displacement or upward delivery.\n       - Oxygen from potassium permanganate (KMnO\u2084): obtained by heating the solid. Potassium permanganate contains no hydrogen; thus liquid water observed at the tube mouth is condensation of water vapor from air or apparatus, not a reaction product.\n     - Misstating the composition of a common compound (e.g., claiming KMnO\u2084 contains hydrogen) is a **Knowledge Error**.\n\n--------------------------------------------------\nGENERAL EVALUATION PRINCIPLES\n--------------------------------------------------\n\n- Always judge the *truth and validity* of the given step in the context of:\n  - The problem statement,\n  - The provided correct final answer (used only to anchor what a correct overall reasoning path looks like),\n  - Standard scientific/mathematical theory at high\u2011school to early undergraduate level.\n\n- Distinguish among:\n  - Purely definitional/background steps (often correct if standard),\n  - Data\u2011dependent steps (may be wrong if they misread graphs or tables),\n  - Inferential steps (may be wrong if the logic is flawed even when formulas are correct).\n\n- When in doubt:\n  - Ask whether there exists at least one consistent, fully correct solution path in which this step would fit as written. If yes, and it does not contradict the problem\u2019s data or theory, mark `True`.\n  - If it contradicts necessity conditions of the problem or known facts, mark `False` and classify the error.\n\n--------------------------------------------------\nOUTPUT FORMAT\n--------------------------------------------------\n\nYour final response must contain **exactly two top\u2011level fields** in this order:\n\n1. `reasoning`  \n   A short, clear explanation as specified above. Do not mention that you \u201creconstructed a solution\u201d or talk about \u201cphases\u201d; just explain the correctness of the step.\n\n2. `correct`  \n   Either `True` or `False` (capitalized, no quotes).\n\nDo **not** include any additional text, JSON keys, headings, or commentary outside these two fields.",
    "fields": [
      {
        "prefix": "Question:",
        "description": "Scientific problem statement."
      },
      {
        "prefix": "Correct Answer:",
        "description": "Correct final answer for the problem."
      },
      {
        "prefix": "Steps:",
        "description": "Full student solution steps."
      },
      {
        "prefix": "Step To Evaluate:",
        "description": "Single step to evaluate for correctness."
      },
      {
        "prefix": "Reasoning:",
        "description": "Reasoning for the binary correctness decision."
      },
      {
        "prefix": "Correct:",
        "description": "Whether the evaluated step is correct."
      }
    ]
  },
  "lm": {
    "model": "gpt-5-mini",
    "model_type": "chat",
    "cache": true,
    "num_retries": 3,
    "finetuning_model": null,
    "launch_kwargs": {},
    "train_kwargs": {},
    "temperature": null,
    "max_completion_tokens": null
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  "metadata": {
    "dependency_versions": {
      "python": "3.11",
      "dspy": "3.1.3",
      "cloudpickle": "3.1"
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}