From what I hear, if you encounter a cougar in the wild, you are supposed to freeze, then slowly walk backwards away from the cougar so it will not feel threatened. This is what a ranger told me when I did a hiking trip when I was in my teens.
See my post above, specifically the link to the video on turning your back to a cat like that.
Worst thing you can do.
Better have a Plan B just in case.
As I suggested elsewhere on the thread, that might or might not work, but running will definitely get you killed.
With cats the idea is to look as big and threatening as possible. Pick up children and put them on your shoulders, it gets them off the ground and makes you look bigger. Pick up a stick, shout, look as tough as you can. Bear you do not make eye contact with and look the least threatening as possible. Unfortunately if you encounter a cat during daylight it is likely rabid. Even running in my semirural neighborhood I always carry....
Actually with a cougar or a lone black bear you are supposed to make yourself as big as you can with a stick or similar because they won’t confront a large aggressive opponent,usually.