Verb meaning to solve problems through precision or accuracy?
Perhaps you are looking for the verb finesse (MW):
to bring about, direct, or manage by adroit maneuvering
finesse his way through tight places
to maneuver TFD
To act with skill or cunning in gaining an end:
As in:
He maneuvered complexity, getting closer and closer to the X.
When I think of to maneuver, stratagems, cunning and purpose of movement come to mind.