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Assorted cures.

Safe Boot from the HD, (holding Shift key down at startup), does the problem occur in Safe Mode?

Safe mode attempts to repair Disks & clears lots of caches, so if Safe Mode works try again in regular boot.

Assuming all your Mail is IMAP & not POP, highlight Inbox, from Mail's Mailbox menu choose Rebuild.

Did you get it fixed?

Great news! :)

The problem remains after booting up ins safe mode.

What can I try next? (This is a very new MacBook Pro)