Based on the given information, it seems that the projector is experiencing issues with overheating or a faulty power supply. The fact that it shuts off and cannot be turned back on until it has cooled down for 15 minutes suggests that the projector is overheating or there is a problem with the power supply. Therefore, the next logical step would be to clean the filter to ensure proper ventilation and airflow, as a dirty filter can cause overheating.