Yes, you can assign tasks to other team members if the task needs to be taken cared of by another user.
All you need to do is click on the post in Inbox, then select Task:
By default the task is assigned to you but you can click on another user to assign it to that person:
If the Send Email Notification is ticked, the user will get an email notification similar to this:
If you have a task assigned to you, you will see your list of Open Tasks when you click on Tasks:
Depending on the task assigned to you, you can leave an internal comment or engage in the activity before completing the task such as respond to a mention, follow a new follower, etc:
Here is a tutorial video on assigning tasks to team members: