We propose a shared autonomy approach for implementing human operator decisions onto an automated system during multi-objective missions, while guaranteeing safety and mission completion. A mission is specified as a set of linear temporal logic (LTL) formulae. Then, using a novel correspondence between LTL and reachability analysis, we synthesize a set of controllers for assisting the human operator to complete the mission, while guaranteeing that the system maintains specified spatial and temporal properties. We assume the human operator's exact preference of how to complete the mission is unknown. Instead, we use a datadriven approach to infer and update the automated system's internal belief of which specified objective the human intends to complete. If, while the human is operating the system, she provides inputs that violate any of the invariances prescribed by the LTL formula, our verified controller will use its internal belief of the human operator's intended objective to guide the operator back on track. Moreover, we show that as long as the specifications are initially feasible, our controller will stay feasible and can guide the human to complete the mission despite some unexpected human errors. We illustrate our approach with a simple, but practical, experimental setup where a remote operator is parking a vehicle in a parking lot with multiple parking options. In these experiments, we show that our approach is able to infer the human operator's preference over parking spots in real-time and guarantee that the human will park in the spot safely.