Number Theory GCD Problem

I have been struggling on this question for way too long, and I just can't figure out what to do. I have tried all of my textbooks already, so I thought someone here might be able to help

The question is as follows:

[note (x,y) denotes GCD]

Let a,b in the integers with (a,b)=1. Find all possible values of (a+3b, b+3a)

All I think I figured out so far is to start by letting d= (a+3b,b+3a) and from there realizing that d|a+3b and d|3a+b .. but i dont know what to do from there. Please help!