Vision-and-Language Navigation (VLN) requires an agent to dynamically explore complex 3D environments following human instructions. Recent research underscores the potential of harnessing large language models (LLMs) for VLN, given their commonsense knowledge and general reasoning capabilities. Despite their strengths, a substantial gap in task completion performance persists between LLM-based approaches and domain experts, as LLMs inherently struggle to comprehend real-world spatial correlations precisely; additionally, LLM inference can make the decision-making process considerably inefficient. To address these issues, we propose a novel dual-process thinking framework dubbed $R^3$, integrating LLMs’ generalization capabilities with VLN-specific expertise in a zero-shot manner. The framework comprises three core modules: Runner, Ruminator, and Regulator. The Runner is a lightweight transformer-based expert model that ensures efficient and accurate navigation under regular circumstances. The Ruminator employs a multimodal LLM as the backbone and adopts chain-of-thought (CoT) prompting to elicit structured reasoning from the LLM. The Regulator monitors the navigation progress and controls the appropriate thinking mode according to three criteria, integrating Runner and Ruminator harmoniously. Experimental results illustrate that R$^3$ significantly outperforms other state-of-the-art methods, exceeding 3.28% and 3.30% in SPL and RGSPL respectively on the REVERIE benchmark, highlighting the effectiveness of our method in handling challenging VLN tasks.