LLM-powered systems require complex multi-step decision-making abilities to solve real-world tasks, yet current planning approaches face a trade-off between the high latency of inference-time search and the limited generalization of supervised fine-tuning. To address this limitation, we introduce SGA-MCTS, a framework that casts LLM planning as non-parametric retrieval. Offline, we leverage Monte Carlo Tree Search (MCTS) to explore the solution space and distill high-fidelity trajectories into State-Goal-Action (SGA) atoms. These atoms are de-lexicalized primitives that abstract concrete entities into symbolic slots, preserving reusable causal logic while discarding domain-specific noise. Online, a retrieval-augmented agent employs a hybrid symbolic-semantic mechanism to fetch relevant SGAs and re-ground them into the current context as soft reasoning hints. Empirical results on complex benchmarks demonstrate that this paradigm enables frozen, open-weights models to match the performance of SOTA systems (e.g., GPT-5) without task-specific fine-tuning. By effectively amortizing the heavy computational cost of search, SGA-MCTS achieves System 2 reasoning depth at System 1 inference speeds, rendering autonomous planning both scalable and real-time feasible.

Dense retrieval, which aims to encode the semantic information of arbitrary text into dense vector representations or embeddings, has emerged as an effective and efficient paradigm for text retrieval, consequently becoming an essential component in various natural language processing systems. These systems typically focus on optimizing the embedding space by attending to the relevance of text pairs, while overlooking the Boolean logic inherent in language, which may not be captured by current training objectives. In this work, we first investigate whether current retrieval systems can comprehend the Boolean logic implied in language. To answer this question, we formulate the task of Boolean Dense Retrieval and collect a benchmark dataset, BoolQuestions, which covers complex queries containing basic Boolean logic and corresponding annotated passages. Through extensive experimental results on the proposed task and benchmark dataset, we draw the conclusion that current dense retrieval systems do not fully understand Boolean logic in language, and there is a long way to go to improve our dense retrieval systems. Furthermore, to promote further research on enhancing the understanding of Boolean logic for language models, we explore Boolean operation on decomposed query and propose a contrastive continual training method that serves as a strong baseline for the research community.