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This CL is intended to be a no-op logic wise (aside from merging
DoWork()/DoDelayedWork() into a single call).

As a follow-up, it might be possible to take better advantage of
NextWorkInfo::recent_now but it wasn't trivial to do so in this pump
since the sleep is not invoked directly from Run() but rather implicit
from HandlePrepare(). We could also potentially reuse |recent_now|
between HandlePrepare() and HandleCheck(). For now we stick to invoking
TimeTicks::Now() as much as the previous impl did.

Bug: 885371
Change-Id: I4f9d6642c44dbad82cb3588cf3f5323ddf9c19ad
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/1594695
Commit-Queue: Gabriel Charette <gab@chromium.org>
Commit-Queue: Mark Mentovai <mark@chromium.org>
Auto-Submit: Gabriel Charette <gab@chromium.org>
Reviewed-by: Mark Mentovai <mark@chromium.org>
Cr-Commit-Position: refs/heads/master@{#656415}