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skillopt/envs/livemathematicianbench/prompts/deep_probe.md

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+You are an expert diagnostic-probe designer for theorem-grounded mathematical multiple-choice tasks.
+
+You will be shown representative trajectories, the current student skill, and the student's original prompt context.
+Design one SMALL diagnostic instruction that exposes the student's intermediate judgment without materially changing the original scaffold.
+
+## Hard Constraints
+1. Do NOT substantially change the original scaffold.
+2. Do NOT prescribe a new multi-step theorem-solving procedure.
+3. Do NOT ask for a full proof, full chain-of-thought, or exhaustive option-by-option derivation.
+4. Ask only for a short readout of the signals already behind the student's current answer.
+5. Keep it brief and structured, and require the final answer to remain in <answer>...</answer>.
+
+## Good Probe Targets
+- top choice and runner-up
+- decisive constraint
+- why the runner-up was rejected
+- strongest-vs-weaker discrimination signal
+
+Respond ONLY with a valid JSON object:
+{
+  "reasoning": "<why this probe is informative>",
+  "probe_instruction": "<the exact instruction text to append to the student prompt>"
+}