E-commerce search relevance is a critical component of retrieval systems. While Large Language Models (LLMs)-driven Chain-of-Thought (CoT) modeling has become the dominant paradigm and yielded significant gains, a critical gap remains: the absence of a systematic definition for comprehensive relevance reasoning, which leads to significant blind spots in current approaches. In this paper, we deconstruct the task into three core competencies: reasoning knowledge, multi-modal understanding, and rule awareness. Accordingly, we propose LoRE(Large Generative Model for Search Relevance), a novel two-stage training framework. We first employ an SFT phase to instill these capabilities via a progressive CoT synthesis pipeline, followed by a Reinforcement Learning(RL) phase, which serves as a regularizer, pruning redundant logic to achieve precise and robust adjudication. Extensive experiments validate LoRE, outperforming GPT-5 by 29.1% in Macro-F1 and achieving a 27% online gain, offering a vital reference for industrial domain-specific post-training.