The current design is,
We have different inbox for different team. A user will have a role specific to that team. A user can see and search the tasks from his team- in all status (New,already claimed by another user,completed etc)
If he searches a New task, he can claim it and do manipulation of the task. He cannot directly claim a task being worked by anyother user. He has to first unlock it and then only claim.
If he has wrongly picked a task and wants to release, he can do that.
Please let me know if you need any details. Thanks.