Specific word for piecing two facts together

Solution 1:

It's not restricted to OP's exact intended sense of find a perspective from which two apparently contradictory facts become mutually compatible, but in practice the most likely term would be...

I don't know how to reconcile his latest statement with his original speech or supposed goals.

From Cambridge Dictionary

reconcile
to find a way in which two situations or beliefs that are opposed to each other can agree and exist together

More informally / idiomatically, there's also (again, from Cambridge Dictionary)...

square (sth) with sth
to match or agree with something, or to think that one thing is acceptable together with another thing