Speed through sounds great in this sentence. Similar descriptions can be: blow through(less formal), accelerate through, quickly complete/finish(sounds less powerful).
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mitsuwao23speed through performance and administration taskscomplete the tasks associated with performance and administration very quickly.
mitsuwao23I didn't realize that "speed" can imply "finishing"As holyduke says, it's not "speed" that connotes finishing; it's "through" that gives that meaning.