'think'
is the mental process you go through pondering upon an issue, a problem and thus form your idea about it or come to a conclusion that you are certain of and convinced of it to be true ,you will express that as :
'I think that it is A.'
'suppose'
Your idea or end result of choosing the problem's solution to be 'A' is not necessarily built on previous mental thinking ,but it depends rather on information you already have about the issue, your experience or knowledge or all of them ,upon which you form your idea, that you probably with a certain degree of certainty believe to be true ,but there remains some elements of doubt and it is not a 100% conviction of your result, it is like saying :
"Built on all my experience and the beforehand evidence I think that it must be A ,but I am not 100% sure though ."
"I suppose it is A."
'assume':
Here you build your assumption that 'A' is the correct choice, while you don't really have any proof, you just believe it is true .Here your choice of 'A' is a hypothesis that you take for granted ,while you have no evidence to prove it. You don't by any means confirm any certainty of your choice, but just express your belief in it .
"I assume it is A'