Recently the emergence of novel presentation attacks has drawn increasing attention to face anti-spoofing. However, existing methods tend to memorize data patterns from the training set, resulting in poor generalization to unknown attack types across different scenarios and limited interpretability. To address these challenges, this paper presents a reinforcement fine-tuning-based face anti-spoofing method that stimulates the capabilities of multimodal large language models to think and learn how to solve the anti-spoofing task itself, rather than relying on the memorization of authenticity patterns. We design verifiable class consistent reward and reasoning consistent reward, and employ a GRPO-based optimization strategy to guide the model in exploring reasoning policies from multiple perspectives to maximize expected rewards. As a result, through iterative trial-and-error learning while retaining only high-reward trajectories, the model distills highly generalizable decision-making rules from the extensive solution space to effectively address cross-domain face anti-spoofing tasks. Extensive experimental results demonstrate that our method achieves state-of-the-art cross-domain generalization performance. It generalizes well to diverse unknown attack types in unseen target domains while providing interpretable reasoning for its authenticity decisions without requiring labor-intensive textual annotations for training.