This study explores the inefficiencies inherent in group decision-making processes, particularly when critical information is dispersed among team members. The limitations of traditional human-based research methods prompt an AI-driven approach to model discussion. CogSystem is designed for simulating group decision-making, examining the interplay between group-level processes and individual-level cognition. The taxonomy comprises of CogFrame, a discussion framework, and CogChain, a cognitive architecture. CogFrame allows for the manipulation of discussion length, information distribution, and decision rules. CogChains are introduced to LLM-based agents to enhance their realism and simulate the cognitive processes influencing contribution of information items. Each CogChain captures a different individual level factor, including motivations, memory, and trust. Combinations of CogFrame and CogChain parameters are tested to investigate their impact on the optimality of the discussion result in the context of the hidden profile. The results offer insights into enhancing behavior modeling, decision-making outcomes, and human-AI collaboration.