Managing your daily priorities using your email inbox is inefficient. Your inbox includes emails that are current tasks as well as requests you have already completed and no longer need your attention. This is why Dossier has two-way sync with Asana. Dossier already helps you with auto-archiving emails related to tasks in Asana.
Now you can close completed Asana tasks directly from your Gmail inbox. Simply apply the blue "Closed" label to the email in Gmail and since Dossier syncs your Gmail inbox and Asana tasks in real time, the thread will be closed across all your apps, for all your team members. If you receive a reply on the email, it will automatically be opened in Asana, get labeled as "Open", and unarchived in your Gmail.