Despite the emergence of advanced technologies, the behavioural complexities remain underexplored, especially from the viewpoint of their potential in interactive installations. This study aims to explore the future interactivity of an agent's behaviour by envisioning speculative future human operations using a human-controlled interactive installation called LumiLand. This empirical study reveals that an agent can craft a user experience by (1) controlling the plot, (2) cocreating content with a user in a social manner, and (3) promptly adjusting undefined behaviours and situations. Based on Janlert and Stolterman's interaction model, we present an interaction flow with four primary classifications: Leading, Responding, Poking, and Linking. We believe that a human-centered approach for understanding agent interactivity could help create entertaining human-computer interactions (HCI) by improving the agent design and exploring the challenges that will be faced during such interactions.