Medical image segmentation is undergoing a paradigm shift from conventional visual pattern matching to cognitive reasoning analysis. Although Multimodal Large Language Models (MLLMs) have shown promise in integrating linguistic and visual knowledge, significant gaps remain: existing general MLLMs possess broad common sense but lack the specialized visual reasoning required for complex lesions, whereas traditional segmentation models excel at pixel-level segmentation but lack logical interpretability. In this paper, we introduce ComLesion-14K, the first diverse Chain-of-Thought (CoT) benchmark for reasoning-driven complex lesion segmentation. To accomplish this task, we propose CORE-Seg, an end-to-end framework integrating reasoning with segmentation through a Semantic-Guided Prompt Adapter. We design a progressive training strategy from SFT to GRPO, equipped with an adaptive dual-granularity reward mechanism to mitigate reward sparsity. Our Method achieves state-of-the-art results with a mean Dice of 37.06\% (14.89\% higher than the second-best baseline), while reducing the failure rate to 18.42\%. Project Page: https://xyxl024.github.io/CORE-Seg.github.io/