Coreference Resolution (CR) is a critical task in Natural Language Processing (NLP). Current research faces a key dilemma: whether to further explore the potential of supervised neural methods based on small language models, whose detect-then-cluster pipeline still delivers top performance, or embrace the powerful capabilities of Large Language Models (LLMs). However, effectively combining their strengths remains underexplored. To this end, we propose ImCoref-CeS, a novel framework that integrates an enhanced supervised model with LLM-based reasoning. First, we present an improved CR method (ImCoref) to push the performance boundaries of the supervised neural method by introducing a lightweight bridging module to enhance long-text encoding capability, devising a biaffine scorer to comprehensively capture positional information, and invoking a hybrid mention regularization to improve training efficiency. Importantly, we employ an LLM acting as a multi-role Checker-Splitter agent to validate candidate mentions (filtering out invalid ones) and coreference results (splitting erroneous clusters) predicted by ImCoref. Extensive experiments demonstrate the effectiveness of ImCoref-CeS, which achieves superior performance compared to existing state-of-the-art (SOTA) methods.