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In particular:
 A) Don't need to ScheduleWork around Run() in
    QuitStopsWorkWithNestedRunLoop
 B) Require GMOCK to verify that all expectations resolve InSequence
 C) Out-of-band invocations of DoIdleWork should only happen *after*
    DoWork (unexpected but loosened on OS_IOS for ignored reasons;
    keeping for now).

This is a prerequisite to make the diff smaller for tests in
https://chromium-review.googlesource.com/c/chromium/src/+/2226216

Bug: 1074019
Change-Id: I0da743e9a6737433a69cdc81669981833fbe6ab0
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/2313697
Commit-Queue: François Doray <fdoray@chromium.org>
Auto-Submit: Gabriel Charette <gab@chromium.org>
Reviewed-by: François Doray <fdoray@chromium.org>
Cr-Commit-Position: refs/heads/master@{#791359}