通过分阶段推理修正，让小模型诊断准确率提升12.7%。

Accurate clinical diagnosis requires extensive domain knowledge and complex clinical reasoning capabilities. Although large language models (LLMs) hold great potential for clinical reasoning, their high computational and memory requirements limit their deployment in resource-constrained environments. Knowledge distillation (KD) can compress LLM capabilities into smaller models, but traditional KD merely transfers superficial answer patterns and fails to preserve the structured reasoning required for reliable diagnosis. To address this, we propose a two-stage distillation framework, MedThink, designed to cultivate robust clinical reasoning in small language models (SLMs). In the first stage, a teacher LLM screens data and injects domain-knowledge explanations to fine-tune a student model, establishing a knowledge foundation. In the second stage, the teacher evaluates the student's errors, generates reasoning chains linking knowledge to correct answers, and refines the student's diagnostic reasoning through a second round of fine-tuning. We evaluate MedThink on general medical benchmarks and a gastroenterology dataset comprising 955 question-answer pairs. Experiments demonstrate that MedThink outperforms six distillation strategies in all benchmarks: achieving an improvement of up to 12.7% over the student baseline in general tasks, and reaching a total top accuracy of 56.4% in gastroenterology evaluation. This indicates that iterative distillation centered on reasoning can significantly enhance the diagnostic accuracy and generalization capabilities of SLMs whilst maintaining computational efficiency. Our code and data are publicly available at https://github.com/destinybird/PrecisionBoost.