Large language models (LLMs) have demonstrated strong potential in long-horizon decision-making tasks, such as embodied manipulation and web interaction. However, agents frequently struggle with endless trial-and-error loops or deviate from the main objective in complex environments. We attribute these failures to two fundamental errors: global Progress Drift and local Feasibility Violation. Existing methods typically attempt to address both issues simultaneously using a single paradigm. However, these two challenges are fundamentally distinct: the former relies on fuzzy semantic planning, while the latter demands strict logical constraints and state validation. The inherent limitations of such a single-paradigm approach pose a fundamental challenge for existing models in handling long-horizon tasks. Motivated by this insight, we propose a Neuro-Symbolic Dual Memory Framework that explicitly decouples semantic progress guidance from logical feasibility verification. Specifically, during the inference phase, the framework invokes both memory mechanisms synchronously: on the one hand, a neural-network-based Progress Memory extracts semantic blueprints from successful trajectories to guide global task advancement; on the other hand, a symbolic-logic-based Feasibility Memory utilizes executable Python verification functions synthesized from failed transitions to perform strict logical validation. Experiments demonstrate that this method significantly outperforms existing competitive baselines on ALFWorld, WebShop, and TextCraft. Code is available at https://github.com/LAMDA-NeSy/DualMemory.

Vision-Language Navigation (VLN) requires an embodied agent to follow natural-language instructions in unseen environments. Recent progress has been largely driven by Multimodal Large Language Models (MLLMs). Existing methods follow a next-step action prediction paradigm, supervising only the expert action, which requires a high quantity of data for training. They also rely on cognitive maps, accumulated historical frames, or external 3D tools to maintain states, leading to high computational and memory overhead. To realize resource efficiency VLN, we propose LookStep, a unified end-to-end framework that combines Language Centric Future State Modeling and Event Driven Rolling Memory that uses language labels to generate coarse-grained navigation progress and future states for each candidate action, while autonomously deciding whether to write each observation into a bounded rolling memory with a semantic role. We validate LookStep empirically. On VLN-CE tasks, LookStep outperforms existing methods under the same training settings, achieving a 49.7% success rate on R2R-CE Val-Unseen with better memory efficiency and less data usage. Code and model is available at https://github.com/kunyang-YU/LookStep.