Hard to imagine a big and relatively slow Great Pyrenees catching an outdoor cat. I’ve had similarly-sized (150 lb) Newfoundlands, and my cats ran rings around them.
Some dogs fake cats out by acting uninterested and bored. Then snip snap they become a feline frisbee.
Our standard poodle was a wizard at taking cats off the top of the six foot fence surrounding our yard when he appeared to be sleeping. That dog was smarter than many humans.