This paper presents a novel approach to improving real-time decision-making in 6G networks by leveraging autonomous agents based on large-scale language models (LLMs). We aim to move beyond traditional AI focused on specific tasks and toward networks based on Artificial General Intelligence (AGI) with broader reasoning capabilities. To achieve this, we propose a novel paradigm called "symbiotic agents," which combine LLMs with real-time optimization algorithms. An input-stage optimizer manages uncertainty for numerically precise tasks, while an output-stage optimizer performs adaptive real-time control under the supervision of the LLMs. We design and implement a multi-agent system for negotiating service-level agreements (SLAs) with a radio access network (RAN) optimizer, and present experimental results using a 5G testbed. Experimental results show that the symbiotic agents reduce decision-making errors by five times compared to single-agent LLMs. Using small-scale language models (SLMs), we achieve similar accuracy while reducing GPU resource usage by 99.9%. A demonstration of multi-agent collaboration on a real-world testbed demonstrates the flexibility of SLAs and resource allocation, reducing RAN over-utilization by approximately 44%.