arXiv:2510.10592v1 Announce Type: new Abstract: Existing studies have introduced method-based reasoning and scope extension as approaches to enhance Large Language Model (LLM) performance beyond direct matrix mappings. Building on these foundations, this paper summarizes and integrates these ideas into a unified Intuition-Method Layered Model with Scope Extension, designed to address indirected (unseen) issues more systematically. In this framework, intuition-based thinking provides rapid first-reaction answers, while method-based thinking decouples questions and solutions into transferable reasoning units. Scope extension is then applied to broaden applicability, including vertical (cause analysis), horizontal (parallel and generalized issues), and for the first time, temporal and spatial extensions, which expand reasoning across time and contextual dimensions. These extensions are organized into systematic knowledge trees that interconnect into a knowledge network, thereby increasing adaptability. To quantitatively evaluate this process, we propose the entropy of method extension, which measures the independence and diversity of extensions as an indicator of the system's capacity to solve unseen questions. By logically connecting existing approaches with new extensions and introducing an entropy-based evaluation framework, this work advances toward a more robust and extensible reasoning paradigm for LLMs in real-world problem-solving.