In object goal navigation (ObjectNav), an embodied agent must find a target object (e.g., "find a bed") in a previously unseen environment, relying on spatial commonsense such as object co-occurrence. Large Language Models (LLMs) encode this commonsense, but deploying them on robots exposes a trade-off between reasoning quality and efficiency: cloud-based models incur latency and privacy risks, whereas small on-device LLMs are fast but prone to hallucinated spatial judgments. Hybrid reasoning LLMs offer both a fast non-thinking mode and a slow thinking mode, which raises a key question for embodied agents: when is slow thinking worth its cost? We propose CovNav, a training-free framework that answers this question with Conformal Prediction (CP), turning dual-process (System 1 / System 2) inference into an uncertainty-aware decision. Much like recent decision models such as Jev, CovNav casts each spatial query as a structured binary decision rather than free-form generation: a local LLM in fast mode judges whether the target is likely near an observed object, CP converts its token probabilities into a prediction set, and only ambiguous queries are escalated to slow chain-of-thought reasoning. The object-pair formulation keeps calibration tractable and supports open-set objects through off-the-shelf detectors. Experiments on Gibson and HM3D show that CovNav surpasses the strongest zero-shot baseline by 0.8 and 1.7 percentage points in success rate on HM3D v1 and v2, while invoking slow reasoning for only 12.4% of queries and retaining most of the gain of always-on thinking at a fraction of its latency. Real-robot experiments on a TurtleBot 4 further validate the approach. CovNav shows how calibrated uncertainty can decide when an embodied agent should think slowly, offering a principled form of adaptive test-time reasoning for LLM-based robots.

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