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This change should not affect any behavior.

This CL moves the change password code out of the coordinator. This
keeps the coordinator clean from any logic and helper code so that it
remains focused on assembling the component and forwarding events.

Bug: 1092444
Change-Id: I2e380cf06403cfe91c39e02e9a65cc3352a44aec
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/2352920
Commit-Queue: Friedrich [CET] <fhorschig@chromium.org>
Reviewed-by: Ioana Pandele <ioanap@chromium.org>
Cr-Commit-Position: refs/heads/master@{#798611}