What is the correct course of action in this situation?

Your answer is fully correct.

In Germany, when approaching a pedestrian crossing, you must watch pedestrians closely because they may step onto the crossing at any moment. You should reduce your speed and be prepared to stop if necessary, to yield right of way to pedestrians. Continuing at the same speed without caution is not allowed, as it endangers pedestrians and violates traffic safety rules.

By watching closely and reducing your speed, you ensure the safety of pedestrians and comply with the legal obligation to yield at pedestrian crossings. This approach helps to prevent accidents and fulfils the rule that drivers must always be prepared to stop for pedestrians at marked crossings.