Negation of 2 things: "and" or "or"?
The negation of both is:
I am not doing A or B.
If you use and, it just means that they aren't both being done. But it could be that neither is being done, or that only one or the other is being done.
In symbolic logic, the negation of a conjunction is represented by something called De Morgan's Laws. (As at the website Brilliant.)
In brief:
Not (A and B) is the same as Not A or Not B.
Not (A or B) is the same as Not A and Not B.