Existing 3D human motion generation and understanding methods often exhibit limited interpretability, restricting effective mutual enhancement between these inherently related tasks. While current unified frameworks based on large language models (LLMs) leverage linguistic priors, they frequently encounter challenges in semantic alignment and task coherence. Moreover, the next-token prediction paradigm in LLMs is ill-suited for motion sequences, causing cumulative prediction errors. To address these limitations, we propose UniMo, a novel framework that integrates motion-language information and interpretable chain of thought (CoT) reasoning into the LLM via supervised fine-tuning (SFT). We further introduce reinforcement learning with verifiable rewards (RLVR), implemented via Group Relative Policy Optimization (GRPO), as a post-training strategy that optimizes over groups of tokens to enforce structural correctness and semantic alignment, mitigating cumulative errors in motion token prediction. Extensive experiments demonstrate that UniMo significantly outperforms existing unified and task-specific models, achieving state-of-the-art performance in both motion generation and understanding.