With the release of OpenAI’s o1 model, reasoning models that adopt slow-thinking strategies have become increasingly common. Their outputs often contain complex reasoning, intermediate steps, and self-reflection, making existing evaluation methods and reward models inadequate. In particular, they struggle to judge answer equivalence and to reliably extract final answers from long, complex responses. To address this challenge, we propose xVerify, an efficient answer verifier for evaluating reasoning models. xVerify shows strong equivalence judgment capabilities, enabling accurate comparison between model outputs and reference answers across diverse question types. To train and evaluate xVerify, we construct the VAR dataset, consisting of multi-round annotated QA pairs generated by multiple LLMs across challenging reasoning tasks. Experimental results on both test and generalization sets show that all xVerify variants achieve over 95% F1 score and accuracy. Notably, the smallest model, xVerify-0.5B-I, outperforms all evaluation methods except GPT-4o, while xVerify-3B-Ib surpasses GPT-4o in overall performance. In addition, reinforcement learning experiments using xVerify as the reward model yield an 18.4% improvement for Qwen2.5-7B compared with direct generation, exceeding the gains achieved with Math Verify as the reward. These results demonstrate the effectiveness and generalizability of xVerify. All xVerify resources are available on [GitHub](https://github.com/IAAR-Shanghai/xVerify).

Cold-start supervised fine-tuning (SFT) is a critical initialization step before reinforcement learning from verifiable rewards (RLVR). Yet existing cold-start data selection methods largely inherit criteria from supervised instruction tuning—sample quality, difficulty, perplexity, or diversity—implicitly assuming that a stronger SFT warm start is also a better starting point for RL. We argue that this assumption does not always hold in the SFT-to-RL pipeline: cold-start SFT not only reduces supervised loss but also shapes the initial update geometry that downstream reward optimization inherits. Building on this observation, we propose RL-Proxy-Coverage. Our method estimates a low-rank, reward-relevant gradient subspace from a small set of representative RL anchor prompts and verifier rewards, and selects, as the cold-start subset, those candidate SFT examples whose gradients provide non-redundant coverage of this subspace. In controlled mathematical-reasoning experiments, RL-Proxy-Coverage outperforms representative SFT-centric, hard-diverse, and reward-aware baselines at the early-to-mid RL checkpoints. Our findings suggest a new view of cold-start data: it should be regarded not merely as supervised examples for improving SFT, but as an initialization resource that shapes the starting point of downstream reward optimization.