Large Language Models (LLMs) have shown remarkable progress across domains, yet their ability to perform inductive reasoning - inferring latent rules from sparse examples - remains limited. It is often assumed that chain-of-thought (CoT) prompting, as used in Large Reasoning Models (LRMs), enhances such reasoning. We investigate this assumption with creating four controlled, diagnostic game-based tasks - chess, Texas Hold'em, dice games, and blackjack - with hidden human-defined rules. We find that CoT reasoning can degrade inductive performance, with LRMs often underperforming their non-reasoning counterparts. To explain this, we present a theoretical framework that reveals how reasoning steps can amplify error through three failure modes: incorrect sub-task decomposition, incorrect sub-task solving, and incorrect final answer summarization. Based on our theoretical and empirical analysis, we introduce structured interventions that adapt CoT generation according to our identified failure types. These interventions improve inductive accuracy without retraining. Our findings suggest that effective (CoT) reasoning depends not only on taking more steps but also on ensuring those steps are well-structured.

Recent works in Task and Motion Planning (TAMP) show that training control policies on language-supervised robot trajectories with quality labeled data markedly improves agent task success rates. However, the scarcity of such data presents a significant hurdle to extending these methods to general use cases. To address this concern, we present an automated framework to decompose trajectory data into temporally bounded and natural language-based descriptive sub-tasks by leveraging recent prompting strategies for Foundation Models (FMs) including both Large Language Models (LLMs) and Vision Language Models (VLMs). Our framework provides both time-based and language-based descriptions for lower-level sub-tasks that comprise full trajectories. To rigorously evaluate the quality of our automatic labeling framework, we contribute an algorithm SIMILARITY to produce two novel metrics, temporal similarity and semantic similarity. The metrics measure the temporal alignment and semantic fidelity of language descriptions between two sub-task decompositions, namely an FM sub-task decomposition prediction and a ground-truth sub-task decomposition. We present scores for temporal similarity and semantic similarity above 90%, compared to 30% of a randomized baseline, for multiple robotic environments, demonstrating the effectiveness of our proposed framework. Our results enable building diverse, large-scale, language-supervised datasets for improved robotic TAMP.