Prompt-based reasoning strategies such as Chain-of-Thought (CoT) and In-Context Learning (ICL) have become widely used for eliciting reasoning capabilities in large language models (LLMs). However, these methods rely on fragile, implicit mechanisms often yielding inconsistent outputs across seeds, formats, or minor prompt variations making them fundamentally unreliable for tasks requiring stable, interpretable reasoning. In contrast, automata-based neuro-symbolic frameworks like RetoMaton offer a more structured and trustworthy alternative by grounding retrieval in symbolic memory with deterministic transitions. In this work, we extend RetoMaton by replacing its global datastore with a local, task-adaptive Weighted Finite Automaton (WFA), constructed directly from external domain corpora. This local automaton structure promotes robust, context-aware retrieval while preserving symbolic traceability and low inference overhead. Unlike prompting, which entangles context and memory in opaque ways, our approach leverages the explicit structure of WFAs to provide verifiable and modular retrieval behavior, making it better suited for domain transfer and interoperability. We evaluate this local RetoMaton variant on two pretrained LLMs LLaMA-3.2-1B and Gemma-3-1B-PT across three reasoning tasks: TriviaQA (reading comprehension), GSM8K (multi-step math), and MMLU (domain knowledge). Compared to the base model and prompting-based methods, augmenting these setups with local RetoMaton consistently improves performance while enabling transparent and reproducible retrieval dynamics. Our results highlight a promising shift toward trustworthy, symbolic reasoning in modern LLMs via lightweight, automaton-guided memory.