Unsupervised methods are widely used to induce latent semantic structure from large text collections, yet their outputs often contain incoherent, redundant, or poorly grounded clusters that are difficult to validate without labeled data. We propose a reasoning-based refinement framework that leverages large language models (LLMs) not as embedding generators, but as semantic judges that validate and restructure the outputs of arbitrary unsupervised clustering algorithms. Our framework introduces three reasoning stages: (i) coherence verification, where LLMs assess whether cluster summaries are supported by their member texts; (ii) redundancy adjudication, where candidate clusters are merged or rejected based on semantic overlap; and (iii) label grounding, where clusters are assigned interpretable labels through a two-stage process that generates and consolidates semantically similar labels in a fully unsupervised manner. This design decouples representation learning from structural validation and mitigates the common failure modes of embedding-only approaches. We evaluate the framework in real-world social media corpora from two platforms with distinct interaction models, demonstrating consistent improvements in cluster coherence and human-aligned labeling quality over classical topic models and recent representation-based baselines. Human evaluation shows strong agreement with LLM-generated labels, despite the absence of gold-standard annotations. We further conduct robustness analysis under matched temporal and volume conditions to assess cross-platform stability. Beyond empirical gains, our results suggest that LLM-based reasoning can serve as a general mechanism for validating and refining unsupervised semantic structure, enabling more reliable and interpretable analysis of large text collections without supervision.