Sugar's inbound email functionality allows emails to be automatically associated with existing cases when the email's subject includes the case macro. When this occurs, it would be helpful for the status of the case to be updated to reflect that a customer's response or input has been received. Additionally, the assigned user can be notified so they know to take action on the case. This article will walk through using workflows to perform both of these actions when an email is automatically added to an existing case.
There is a knowledge base article that discusses this via non-advanced workflows. Can this be done via Advanced Workflows?