Large language models (LLMs) can reason over both structured measurements and free-text records, which makes them attractive for emergency department (ED) prediction. However, most existing LLMs still fall short of conventional ML methods like trees on EHR-based prediction tasks. Our controlled analysis traces this gap to two weaknesses: LLMs do not select informative features, and they misjudge what numerical values imply for risk even when given the right features. We propose TIR-EC, a tool-integrated reinforcement learning framework that addresses both. TIR-EC exposes EHR feature groups as tools the LLM can call. It trains the LLM with rewards from a gradient-boosted tree teacher, which provides a reference set of informative tools and a graded risk target. TIR-EC also distills task-specific clinical skills into the model weights through a reverse curriculum that gradually removes the skills from the prompt during RL process. Evaluation on three clinical prediction tasks shows that our 4B agent achieves the highest macro F1 of all compared models, outperforms conventional ML baselines, and is competitive with much larger frontier LLMs. Further analysis shows that TIR-EC selects more useful evidence with fewer tool calls and combines measurements more effectively.

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