Great question. You’re right… key of Am. By the way you asked (circle of 5ths, etc.).
I see an opportunity for a some additional coaching here.
I can tell you’re trying to reason it out.
A big shift for me as a musician happened when I began to use my ears first, and let my intellect confirm and fill in. Easier said then done for us adults.
With that said, listen to the progression and see if you can hear the Am as a resting or home chord.
Read this when you get a chance: http://www.tomasmichaud.com/first-secret-playing-awesome-guitar-violate-peril/
BTW… it would be analysed as i – viib – iv – V (the V is altered to fit the role of a dominant chord).