Means-Ends Analysis Helps LLMs Plan in Continuous-State Domains

LLM planning research has traditionally focused on discrete-state domains, where actions form a finite, enumerable set. Existing LLM planning frameworks largely assume actions are enumerable, modeling planning as a search process over candidate actions. However, in continuous-state domains, where actions form a continuum and cannot be enumerated, this assumption breaks down. We find a remedy in Newell and Simon's Means-Ends Analysis (MEA), a general problem-solving technique rooted in heuristics from human psychology. We develop Medaka, an MEA-inspired structured prompting framework that encourages recursive goal decomposition, algebraic derivation, and per-step state tracking. To evaluate native LLM planning abilities in continuous-state domains, we develop Liquidworld, a systematic testbed on liquid mixing. On Liquidworld, Medaka can improve performance across model families, suggesting that classical means-ends analysis elicits LLM-native reasoning abilities that are helpful for continuous-state planning.