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Users can start a cast session from the GMC dialog by clicking on the
cast sinks in the device selector list.
After a new session is started, the local media notification will be
hidden, and the cast media notification will show up in the dialog.

Bug: b/161610050, 1107162
Change-Id: Ia3ad0634f0a45159ed92581ca2c6f097566c1a72
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/2422737Reviewed-by: Tommy Steimel <steimel@chromium.org>
Reviewed-by: Takumi Fujimoto <takumif@chromium.org>
Commit-Queue: Muyao Xu <muyaoxu@google.com>
Cr-Commit-Position: refs/heads/master@{#812353}