What is the correct course of action in this situation?

You answered correctly. When approaching a pedestrian crossing where people are waiting, you must watch the pedestrians closely and reduce your speed, preparing to stop if necessary. This is required by German traffic law to ensure pedestrian safety at marked crossings. You should never simply continue at the same speed, as you must be ready to yield if the pedestrians step onto the crosswalk. Remember, always be cautious when approaching crossings and prioritize pedestrian safety.