The formation of coherent, effective, and equitably sized user groups is a critical and persistent challenge in the design of online social platforms, collaborative learning environments, and enterprise-level teamwork tools. Existing automated methods, while scalable, often fail to produce groups of a consistent, predetermined size, leading to significant logistical issues and imbalanced user experiences. Furthermore, they often rely on shallow or easily manipulated user data. This paper introduces Octapar, a novel, multi-stage algorithmic framework designed to generate semantically coherent, perfectly balanced user clusters from deep, multi-modal user profiles. The framework pioneers a conversational onboarding process, using specialized chatbots and Large Language Models (LLMs) to extract nuanced user characteristics across both skill and philosophical domains. These characteristics are formalized as a rich set of semantic tags. The core technical innovation is a custom weighted attention mechanism that generates a sophisticated user vector by incorporating not only global tag rarity (IDF) but also a novel metric of local, intra-user tag uniqueness. This allows the model to identify and amplify a user's most distinctive traits. Final group formation is achieved via an iterative, assignment-based clustering algorithm that utilizes the Hungarian method to guarantee perfectly balanced clusters. This approach ensures structural consistency and fairness in group formation, a critical and often unmet requirement for many practical applications. We provide a detailed walkthrough of the architecture, the mathematical foundations of its components, and a discussion of its implications for the future of computational group formation.