feat: add mirror question generation with canonical distinctness check

store/prompts/question_gen/ar_mirror_question.md

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+You generate a MIRROR (axis-flipped) version of a video Action Recognition
+multiple-choice question, using the SAME video material.
+
+## Given
+- The original question, its four options, and the correct answer.
+- The flip axis (e.g. "before/after" or "first/last").
+- Subtitle context and video frames.
+
+## Rules
+- Flip ONLY the given axis: turn "before X" into "after X", "first" into
+  "last", etc. Everything else (subject, granularity, style) stays identical.
+- The mirror question MUST have a genuinely DIFFERENT correct answer than the
+  original — it asks about the opposite side of the same axis.
+- Reuse the SAME candidate option texts where possible, re-shuffled; the letter
+  of the correct option WILL differ from the original.
+- If the axis cannot be flipped into a well-formed question with a distinct
+  correct answer (e.g. list-style or "cannot determine" answers), output
+  {"mirror": null}.
+
+## Output
+Respond with ONLY a JSON object:
+```json
+{"mirror": {"question": "...", "options": ["A. ...", "B. ...", "C. ...", "D. ..."], "answer": "C"}}
+```
+Or {"mirror": null} if no valid mirror exists.