If I Thought I Can Do it, ....

I wonder if "If I thought I can do it, ..." is possible at all in a situation, as a derivative of "If I thought 'I can do it,'..." Can anyone think of any situation where you can say "If I thought I can do it, ..."?
(Please assume 'thought' here is the past subjunctive 'thought' for the unreal action)

Sure!

If I thought, "I can do it..."

But no, not really as a straight conditional sentence. At least, nothing comes to mind. Seems like there's a certain amount of verb agreement that has to happen between two halves of a conditional sentence. It you start out with the past tense "thought", you're pretty obligated to finish up with the conditional "could". (I guess could is also the future of can, but here we're using it more as the conditional.) If you go to the present for the first part, you can use it again in the second half: "If I think I can do it." But it would be awkward to try to mix and match past and present.

There are other tense variations you can throw in like "If I had thought I could..." and the like, but they still keep that basic verb agreement going.