Large language models (LLMs) are largely static and often redo reasoning or repeat mistakes. Prior experience reuse typically relies on external retrieval, which is similarity-based, can introduce noise, and adds latency. We introduce SEAM (Structured Experience Adapter Module), a lightweight, executor-specific plug-in that stores experience in its parameters and generates a structured, instance-tailored experience entry in a single forward pass to guide a frozen LLM executor. SEAM is trained for utility via executor rollouts and GRPO while keeping the executor frozen, and can be further improved with logged-success SFT after deployment. Experiments on mathematical reasoning benchmarks show consistent accuracy gains across executors with low overhead. Extensive ablation and analysis further elucidate the mechanisms underlying SEAM’s effectiveness and robustness.[We release our code at <https://anonymous.4open.science/r/SEAM>.]