Just decided to add something:
As to брать/взять, they are a fake pair as well. There WAS a word "взимать" which means to "take away" like take away duties / taxes etc. And this word is a true aspect partner for взять. But now брать/взять are referred as a pair for some reason. Maybe because of their close meaning. Maybe because брать doesn't have a partner, maybe because all of it together.
So the meaning of the принимать/принять word is more like you don't make any physical efforts to take something. Like if someone's giving something to you. Or when you do not make physical actions to make something given your own. Like a king doesn't make any physical action to "receive" tributes.
And брать/взять are supposed to mean that you do something mechanically to actually "take" something. Like taking a book from the table or something.