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Behavioral biometrics have emerged as a promising complement to traditional physiological biometrics by leveraging dynamic human characteristics. These modalities offer advantages including continuous authentication, inherent liveness detection, and greater resistance to credential theft and other spoofing attacks. However, existing systems remain limited in adaptability, contextual awareness, and semantic reasoning as they primarily rely on similarity metrics, static thresholds, or supervised classifiers. As a result, they often struggle with real-world conditions such as behavioral variability, environmental changes, contextual changes, and adversarial manipulations. To address these limitations, we systematically integrate LLM-based contextual reasoning into behavioral biometric authentication. LLMs provide capabilities in contextual inference, sequential reasoning, multimodal understanding, and adaptive decision-making. Building on these strengths, we integrate a lightweight LLM-based reasoning module with a novel phone-blowing behavioral biometric technique to develop a context-aware authentication framework. To this end, we first collect blow-acoustic signals from participants and systematically extract spectral and temporal features. These features are aggregated and converted into comparable similarity representations, using either discrete rule-based categories or continuous normalized scores, which are transformed into structured prompts through prompt engineering. We experimentally evaluate the proposed framework using blow-acoustic data collected from 50 participants under diverse behavioral and contextual conditions. The proposed framework achieves 99.46% and 99.38% authentication accuracy in the rule-based and score-based modes, respectively, outperforming its non-LLM counterpart while maintaining strong robustness under dynamic real-world conditions.