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Prevalent reinforcement learning~(RL) methods for fine-tuning LLM reasoners, such as GRPO or Leave-one-out PPO, abandon the learned value function in favor of empirically estimated returns. This hinders test-time compute scaling that relies on using the value-function for verification. In this work, we propose RL$^V$ that augments any ``value-free'' RL method by jointly training the LLM as both a reasoner and a generative verifier using RL-generated data, adding verification capabilities without significant overhead. Empirically, RL$^V$ boosts MATH accuracy by over 20\% with parallel sampling and enables $8-32\times$ efficient test-time compute scaling compared to the base RL method. RL$^V$ also exhibits strong generalization capabilities for both easy-to-hard and out-of-domain tasks. Furthermore, RL$^V$ achieves $1.5-2\times$ higher performance when jointly scaling parallel and sequential test-time compute with a long reasoning R1 model.