In an era where vast amounts of data are collected and processed from diverse sources, there is a growing demand for sophisticated AI systems capable of intelligently fusing and analyzing this information. To address these challenges, researchers have turned towards integrating tools into LLM-powered agents to enhance the overall information fusion process. However, the conjunction of these technologies and the proposed enhancements in several state-of-the-art works followed a non-unified software architecture, resulting in a lack of modularity and terminological inconsistencies among researchers. To address these issues, we propose a novel LLM-based Agent Unified Modeling Framework (LLM-Agent-UMF) that establishes a clear foundation for agent development from both functional and software architectural perspectives, developed and evaluated using the Architecture Tradeoff and Risk Analysis Framework (ATRAF). Our framework clearly distinguishes between the different components of an LLM-based agent, setting LLMs and tools apart from a new element, the core-agent, which plays the role of central coordinator. This pivotal entity comprises five modules: planning, memory, profile, action, and security -- the latter often neglected in previous works. By classifying core-agents into passive and active types based on their authoritative natures, we propose various multi-core agent architectures that combine unique characteristics of distinctive agents to tackle complex tasks more efficiently. We evaluate our framework by applying it to thirteen state-of-the-art agents, thereby demonstrating its alignment with their functionalities and clarifying overlooked architectural aspects. Moreover, we thoroughly assess five architecture variants of our framework by designing new agent architectures that combine characteristics of state-of-the-art agents to address specific goals. ...