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The general idea here is to encapsulate more of the hotseat's behavior
into its own class rather than have it all over the shelf layout
manager. Eventually, I hope to get rid of the huge
"CalculateHotseatState" method by setting the hotseat state to the
appropriate values from the relevant places.

Change-Id: I03bf50bc9f6fb68f7f22f1b6ec966f08f48220da
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/1893997
Commit-Queue: Manu Cornet <manucornet@chromium.org>
Reviewed-by: Xiyuan Xia <xiyuan@chromium.org>
Cr-Commit-Position: refs/heads/master@{#711796}