Aspect Sentiment Quad Prediction (ASQP) is a fundamental yet challenging task in fine-grained sentiment analysis, particularly when aspects or opinions are implicit. Existing methods often lack explainability and generalization, making it difficult to justify inference decisions and to detect implicit sentiment across domains and varied expression patterns. To address these limitations, we propose Tree-CoT-RT, an explainable multi-path tree-guided chain-of-thought and reinforcement learning framework specifically designed for ASQP. The core idea is to use sentiment tree structures to design type-specific reasoning templates that guide LLMs in generating explainable chains, including both final sentiment quadruples and intermediate inference steps for transparent implicit reasoning. However, the generated reasoning chains often vary in quality and may contain logical inconsistencies. To mitigate this, we introduce a reinforcement learning strategy with a rule-based reward function to generate high-quality reasoning traces, which are then used to fine-tune the LLM and enable controlled sampling. Experiments on benchmark datasets demonstrate that Tree-CoT-RT substantially outperforms strong baselines, particularly in scenarios involving implicit sentiment analysis.