Gaze cues play an important role in human communication and are used to coordinate turn-taking and joint attention, as well as to regulate intimacy. In order to have fluent conversations with people, social robots need to exhibit humanlike gaze behavior. Previous Gaze Control Systems (GCS) in HRI have automated robot gaze using data-driven or heuristic approaches. However, these systems tend to be mainly reactive in nature. Planning the robot gaze ahead of time could help in achieving more realistic gaze behavior and better eye-head coordination. In this paper, we propose and implement a novel planning-based GCS. We evaluate our system in a comparative within-subjects user study (N=26) between a reactive system and our proposed system. The results show that the users preferred the proposed system and that it was significantly more interpretable and better at regulating intimacy.