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Compositional Zero-Shot Learning (CZSL) aims to combine known attributes and objects as primitives for recognizing previously unseen attribute-object pairs. Prior works either predict attributes and objects independently, missing their strong contextual dependency, or use unidirectional conditional modeling (e.g., object-guided attribute prediction), which is prone to error propagation. We propose PRPC, a Progressive Reasoning framework with Primitive Correction, which explicitly models the bidirectional dependency between attributes and objects via step-wise inference. PRPC performs mutual correction of primitives to suppress prediction errors in earlier steps. Specifically, we formulate CZSL as structured, Q&A-style Chain-of-Thought reasoning process and constrain the MLLM to follow predefined semantic steps to generate intermediate decisions. To further enhance the reliability and logical consistency of intermediate reasoning, we introduce reinforcement learning post-training with a GRPO-based objective, providing step-level rewards aligned with the progressive inference procedure. Extensive experiments on three CZSL benchmarks demonstrate that PRPC achieves state-of-the-art performance, validating the effectiveness of progressive reasoning and bidirectional correction for robust compositional generalization.