Large language models achieve remarkable performance via extended chain-of-thought (CoT) reasoning, yet this lengthy process incurs substantial inference overhead. Existing CoT compression methods struggle with inflexible manual length budgets, computationally expensive multi-stage training pipelines, and fragile scalability restricted to small models. We propose **HMPO** (**H**ybrid **M**edian-length **P**olicy **O**ptimization), a cost-effective, single-stage reinforcement learning framework. HMPO efficiently compresses CoT via three synergistic components: an *adaptive median-based budget* derived from successful rollouts to eliminate manual tuning, a *cosine-decay token reward* for smooth length penalization, and a *multiplicative reward formulation* that substantially mitigates trivial reward hacking by strictly prioritizing answer correctness. Trained exclusively on mathematical data, HMPO generalizes seamlessly across math, code, science, and instruction-following tasks. Extensive experiments scaling from 9B to 122B parameters across dense and Mixture-of-Experts (MoE) architectures demonstrate that HMPO achieves **19%–46% token compression with negligible accuracy degradation**, all while drastically reducing training costs compared to existing multi-stage baselines.

Medication recommendation is a crucial task for intelligent healthcare systems. Previous studies mainly recommend medications with electronic health records (EHRs). However, some details of interactions between doctors and patients may be ignored or omitted in EHRs, which are essential for automatic medication recommendation. Therefore, we make the first attempt to recommend medications with the conversations between doctors and patients. In this work, we construct DIALMED, the first high-quality dataset for medical dialogue-based medication recommendation task. It contains 11, 996 medical dialogues related to 16 common diseases from 3 departments and 70 corresponding common medications. Furthermore, we propose a Dialogue structure and Disease knowledge aware Network (DDN), where a QA Dialogue Graph mechanism is designed to model the dialogue structure and the knowledge graph is used to introduce external disease knowledge. The extensive experimental results demonstrate that the proposed method is a promising solution to recommend medications with medical dialogues. The dataset and code are available at https://github.com/f-window/DialMed.