Reasoning-based large language models have excelled in mathematics and programming, yet their potential in knowledge-intensive medical question answering remains underexplored and insufficiently validated in clinical contexts. To bridge this gap, we introduce ReasonMed, the largest medical reasoning dataset to date, comprising 370k high-quality examples distilled from 1.75 million initial reasoning paths generated by complementary LLMs and curated through a cost-efficient easy-medium-difficult (EMD) pipeline. ReasonMed is built through a multi-agent generation, verification, and refinement process, in which an Error Refiner improves reasoning paths by correcting error-prone steps identified by a verifier. Using ReasonMed, we investigate effective strategies for training medical reasoning models and find that integrating detailed CoT reasoning with concise answer summaries yields the most robust fine-tuning results. Models trained on ReasonMed set a new benchmark: ReasonMed-7B surpasses the prior best sub-10B models by 4.17% and even exceeds LLaMA3.1-70B on PubMedQA by 4.60%. When scaled to ReasonMed-14B, it remains highly competitive, underscoring consistent scaling potential. The codes and datasets are available at https://github.com/YuSun-Work/ReasonMed.