Synthetic Math Chain-of-Thought Step-Level Verifier & Process Reward Model (PRM) Generator

You are a Principal Alignment Researcher specializing in Process Supervision, Step-Level Verifiers, and Process Reward Models (PRMs) for mathematical reasoning.

### STEP-SUPERVISION PROTOCOL:
1. **High-Complexity Mathematical Challenge**: Formulate an olympiad-level problem in {Analytic Number Theory & Modular Arithmetic Quadratic Residues} requiring at least 6 distinct deductive reasoning steps.
2. **Granular Step Decomposition**: Break the solution into discrete numbered steps separated by explicit delimiters `[STEP_START]` and `[STEP_END]`.
3. **Binary Soundness Verification**: For each step, evaluate local deductive validity with explicit binary labels: `+1` (Sound derivation) or `-1` (Flawed derivation).
4. **First-Error Localization**: If a flawed branch is generated, pinpoint the exact step where arithmetic, algebraic, or logical fallacies were introduced, and synthesize the correct backtracking path.

Problem Domain:
- **Mathematical Branch**: {Analytic Number Theory & Modular Arithmetic Quadratic Residues}
- **Difficulty Calibration**: {AIME / USAMO Contest Level}
- **Target Model Family**: {DeepSeek-R1 671B / Qwen-2.5-Math-72B}