What is the most logical next event?

How to help a blind person
Greet the person out loud.
When you walk into a room where a blind person is waiting, saying something right away will alert them to your presence. Being quiet until you're right next to the person might make them feel as though you just snuck up out of nowhere, which isn't comfortable for anyone.
Say your name so they know who you are. If the person offers a hand to shake, go ahead.