Do language models understand problems before solving them?

Current LLM math solvers jump straight to planning how to solve a problem. This work inserts an earlier stage where the model first identifies what type of problem it is, which tools apply, and what pitfalls to avoid—before any planning happens. A spoiler-detection filter builds clean training data, and a reward function ensures the plan actually follows from the problem understanding. Tested on four model sizes and five math benchmarks, it wins on 39 of 40 metrics.