Robotic foundation models require reasoning over complex visual scenes to execute adaptive actions in dynamic environments. While recent studies on latent-reasoning Vision-Language-Action (VLA) models have demonstrated the capability to capture fine-grained physical dynamics, they remain predominantly confined to static imitation learning, severely limiting their adaptability and generalization. In this paper, we present LaST-R1, a novel reinforcement learning (RL) post-training framework designed to effectively harness "latent reasoning-before-acting" policies. Specifically, we propose Latent-to-Action Policy Optimization (LAPO), a core RL algorithm that jointly optimizes the latent reasoning process and the action generation. By explicitly embedding latent Chain-of-Thought (CoT) reasoning directly within the RL optimization loop, LAPO stimulates profound physical world modeling, which in turn drives robust execution in interactive environments. Furthermore, an adaptive latent CoT mechanism is introduced, allowing the policy to dynamically modulate its reasoning horizon based on diverse environment states. Experiments show that LaST-R1 achieves a near-perfect 99.9% average success rate on the LIBERO benchmark with only one-shot supervised warm-up, significantly improving convergence speed and performance over prior state-of-the-art (SOTA) methods. In real-world deployments, LaST-R1 yields up to a 22.5% average improvement over SOTA supervised fine-tuning approach across four complex tasks, including both single-arm and dual-arm settings. Finally, LaST-R1 demonstrates strong generalization across simulated and real-world environments.

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