It’s possible to complete the tasks you assigned by ticking the checkboxes:
Both comments will be checked
Also, in case you remember something, or find out that the task had not been finished you can reopen it. Both after completion and reopening of the task, all participants get notified by email.
For your Action Emails and SMS there are some prepared messages: "Task Completed" and and for "Task Reopened". Also, if needed, there is task reminder too.