We present a substantial extension of our Human-Aware Task Planning framework, tailored for scenarios with intermittent shared execution experiences and significant belief divergence between humans and robots, particularly due to the uncontrollable nature of humans. Our objective is to build a robot policy that accounts for uncontrollable human behaviors, thus enabling the anticipation of possible advancements achieved by the robot when the execution is not shared, e.g. when humans are briefly absent from the shared environment to complete a subtask. But, this anticipation is considered from the perspective of humans who have access to an estimated model for the robot. To this end, we propose a novel planning framework and build a solver based on AND-OR search, which integrates knowledge reasoning, including situation assessment by perspective taking. Our approach dynamically models and manages the expansion and contraction of potential advances while precisely keeping track of when (and when not) agents share the task execution experience. The planner systematically assesses the situation and ignores worlds that it has reason to think are impossible for humans. Overall, our new solver can estimate the distinct beliefs of the human and the robot along potential courses of action, enabling the synthesis of plans where the robot selects the right moment for communication, i.e. informing, or replying to an inquiry, or defers ontic actions until the execution experiences can be shared. Preliminary experiments in two domains, one novel and one adapted, demonstrate the effectiveness of the framework.