How can i make it so regular users can ONLY mark tasks assigned to them as Complete

We are having an occasional issue where user A is marking user B's tasks complete - possibly by accident. 

How can i make it so regular users can ONLY mark tasks assigned to them as Complete?

I've tried changing it so all users only have View access, which seems to fix the above problem, but then we have the following problem:

User A uploads document for user B to send out a proof. Since User B only has view access, they cannot "generate proof" for them to create a proof, they'd need to download that original document, then reupload it as a proof.