Add note to tickets that are auto closed

Trying to work out a way of adding a note for a ticket that has been auto closed.

After having 3 unsuccessful attempts at getting a response from a customer, we will move the ticket to a status called "Unanswered".

This status type is set to auto close after 5 business hours.

I would like to be able to add a note to the ticket stating that it was auto-closed by System due to no response, so the customer doesn't have any reason to contact us and scream down the phone about their ticket being closed without consultation, the note will say it - closed due to no response.

There doesn't seem to be anything in the action rules that will help... grateful for any ideas!

Thanks,

Peter