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This refactoring simplifies some manual bookkeeping. It also is
helpful for adding the Stop() function, in the next commit.

Bug: 1092329
Change-Id: I34494155ea161d3e2a0358b6b3d09b40aef85fac
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/2257089Reviewed-by: Kinuko Yasuda <kinuko@chromium.org>
Reviewed-by: Sophie Chang <sophiechang@chromium.org>
Reviewed-by: Tarun Bansal <tbansal@chromium.org>
Commit-Queue: Matt Falkenhagen <falken@chromium.org>
Cr-Commit-Position: refs/heads/master@{#781183}