Early termination questions

Hi, newbie question here
Our tenant decided to move out in the middle of the lease. According to lease, he’s responsible for payment until the end of the terms (06-30-15) unless we re-rent the place.
He did not give us written termination notice, but verbally provided tentative move-out date so we can advertise property while he still lives there.
How would you handle situation like that? What proper steps should I do to protect myself from losses and hold current tenant responsible?
Thanks,
T.

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