Reconstructing precise CAD modeling sequences from point clouds remains a challenging task, especially for objects with complex geometry and topology. In this paper, by formulating the CAD sequence reconstruction as a Markov decision process, we introduce ReACT, a novel Reward-informed Autoregressive decision Cad Transformer architecture for robust CAD sequence prediction. Beyond previous imitation-only approaches, our key innovation is to frame the CAD Transformer under a reinforcement learning paradigm and thereby integrate reward-inspired heuristic learning into our architecture. This allows ReACT to effectively leverage shape-aware long-term reward feedback to guide the inference of (nearly) optimal CAD commands. Specifically, conditioned on past tokens, comprising the historical CAD states, sketch-extrude commands (i.e., actions) and associated geometric rewards, ReACT autoregressively outputs the most promising CAD commands in a causal manner. In particular, we develop a novel scaffold-aware CAD state representation that integrates global point-command features with an incrementally constructed surface point scaffold, enabling fine-grained geometric reasoning for subsequent reconstruction prediction. Moreover, an effective local barrel points-guided dense reward function is designed to jointly evaluate surface fidelity and command efficiency for reliable reward guidance. Extensive evaluations on the DeepCAD and Fusion360 benchmarks demonstrate that ReACT can achieve superior CAD reconstruction quality, even for objects with complex shapes.