Rapid advancements in sixth-generation (6G) networks and large language models (LLMs) have paved the way for ubiquitous intelligence, wherein seamless connectivity and distributed artificial intelligence (AI) have revolutionized various aspects of our lives.However, realizing this vision faces significant challenges owing to the fragmented and heterogeneous computing resources across hierarchical networks, which are insufficient for individual LLM agents to perform complex reasoning tasks.To address this issue, we propose Collaborative Orchestration Role at Edge (CORE), an innovative framework that employs a collaborative learning system in which multiple LLMs, each assigned a distinct functional role, are distributed across mobile devices and tiered edge servers. The system integrates three optimization modules, encompassing real-time perception,dynamic role orchestration, and pipeline-parallel execution, to facilitate efficient and rapid collaboration among distributed agents. Furthermore, we introduce a novel role affinity scheduling algorithm for dynamically orchestrating LLM role assignments across the hierarchical edge infrastructure, intelligently matching computational demands with available dispersed resources.Finally, comprehensive case studies and performance evaluations across various 6G application scenarios demonstrated the efficacy of CORE, revealing significant enhancements in the system efficiency and task completion rates. Building on these promising outcomes, we further validated the practical applicability of CORE by deploying it on a real-world edge-computing platform,that exhibits robust performance in operational environments.