***** NOT A TEACHER *****
1. I think that I understand the problem.
2. The second clause, I believe, is independent.
3. Native speakers often omit words. (It is called "ellipsis.")
4. Thus, I am sure that you have already guessed what I am going to say:
"John must have been playing football, and Mary [must have been] doing her homework."
5. For example, "You love English grammar, and I too." That is, "You love English grammar, and I [love English grammar] too."