What is the most logical next event?

How to greet a cat
Wait for the cat to approach.
When you are near a cat that you are friendly with (e.g. your own, or a close friend's cat) wait for it to approach you. Even cats that are normally friendly have days when they do not wish to be disturbed.
Wait for it to demonstrate signs of affection (e.g. rubbing up against your leg) before greeting it.