That is your choice but I believe the test for mandamus is excessively delayed or similar concept. Ten months - barely current estimated processing time.
Mandamus timelines - think two-three or more standard deviations, not "more than average."
This is to have chance of succeeding in mandamus. Of course many hope the demand letter will work on its own.
My info based on what I've heard. YMMV. And it's your dime, of course.