Optimal meeting time selection based on user constraints expressed in natural language is a challenging decision support problem characterized by implicit and dynamic preferences. This paper investigates interaction strategies with large language models (LLMs) to address this challenge. Two fundamentally different strategies are analyzed: (1) an agentic approach based on generating formal constraints, followed by solving the resulting optimization problem using an external algorithm, and (2) a direct generation approach that obtains a solution from the model in the form of time slots, intervals, or a binary vector. The evaluation is performed using a specially constructed dataset of 100 synthetic queries and the corresponding reference constraints. The results show that the agentic approach demonstrates the highest quality and stability, especially as the number of preferences increases. At the same time, direct generation strategies prove effective when dealing with a small number of constraints and simple formulations, highlighting the importance of selecting an appropriate interaction format with LLMs in practical intelligent systems. These findings open avenues for creating flexible and adaptive scheduling interfaces powered by modern language models.