Long-CoT reasoning combined with reinforcement learning for large language models demonstrates remarkable performance and scalability. However, we observe that the initial policy model could significantly influence the final performance as well as the token efficiency. Additionally, there is a lack of systematic guidelines for obtaining a better initial policy model. To bridge this gap, we initiate a comprehensive investigation by activating the initial model using a variety of datasets with different data volumes and reasoning patterns. Then, we conduct a thorough analysis and comparison of the RL process for different initial models from the perspectives of upper bounds, diversity, and token efficiency, providing a deeper understanding and insight into the long-CoT RL. Based on our empirical results, we propose a systematic guideline and a novel Re-RFT method for constructing a better RL start point. Our experiment results based on the 14B model surpass the DeepSeek-R1-Distill-Qwen-14B by an average of 4.6%, demonstrating our approach’s effectiveness and superiority.

Self-Consistency samples diverse reasoning chains with answers and chooses the final answer by majority voting. It is based on forward reasoning and cannot further improve performance by sampling more reasoning chains when saturated. To further boost performance, we introduce backward reasoning to verify candidate answers. Specifically, for mathematical tasks, we mask a number in the question and ask the LLM to answer a backward question created by a simple template, i.e., to predict the masked number when a candidate answer is provided. Instead of using forward or backward reasoning alone, we propose **FOBAR** to combine **FO**rward and **BA**ckward **R**easoning for verification. Extensive experiments on six standard mathematical data sets and three LLMs show that FOBAR achieves state-of-the-art performance. In particular, FOBAR outperforms Self-Consistency, which uses forward reasoning alone, demonstrating that combining forward and backward reasoning is more accurate in verification. In addition, FOBAR achieves higher accuracy than existing verification methods, showing the effectiveness of the simple template used in backward reasoning and the proposed combination.