What is the correct course of action in this situation?

Your answer to stop and allow the pedestrian to cross is correct. According to German traffic rules, drivers must always give way to pedestrians at pedestrian crossings or when a pedestrian is about to step onto the road from the sidewalk. This is essential for pedestrian safety and to avoid accidents. Flashing headlights or passing with clearance is not appropriate because it may confuse or endanger the pedestrian. Stopping fully ensures the pedestrian can cross safely, and it is a legal requirement in such situations. Keep this rule in mind to protect vulnerable road users and comply with traffic laws.