When you come to a pedestrian crossing with someone already there, do you wait patiently, assuming that they have pressed the button, or do you push the button?

When you come to a pedestrian crossing with someone already there, do you wait patiently, assuming that they have pressed the button, or do you push the button? I tend to push the button, but that doesn't stop me feeling guilty about it. I feel that I am indicating to the other individual that I think they are too stupid to have pushed it. Would the same thing happen with accidents? If you come across an accident with someone already there, do you call the police, or do you assume they've already been called?