What's the difference between achieve and reach? When are they interchangeable?

Reach (verb) means extend your arm to take something in your hand. It is only with a figurative meaning that it is the same as achieve. This figurative meaning is less formal and so more common in spoken English than achieve.

You can either reach or achieve your goal, you can reach a higher plane, but you can only reach something on the top shelf.

I’m not sure the words are at all interchangeable. Can you describe a situation where you think they are or might be?