To "rarely act without thinking" means that the person almost always thinks carefully before doing something and that they hardly ever act without having thought about it first. It's the best way to do something ~ think first, act later.
[To "act without thinking" is to jump the gun and do something on the spur of the moment without having given any thought to what they were about to do. (acting first and thinking afterwards) This can often have negative results!]
[To "act without thinking" is to jump the gun and do something on the spur of the moment without having given any thought to what they were about to do. (acting first and thinking afterwards) This can often have negative results!]