Prioritizing - Group Project vs Individual Project

Curious as to others opinions -

If you have two work deliverables due on the same day - one deliverable is a group type item for example a larger deliverable in which 3 separate individuals are working a portion and the deliverable requires all 3 to complete and signoff and a second deliverable which is just your own responsibility.

You can complete them both within the time frame - might take you a little beyond the normal 9-5 but not significantly later.

Which do you try to complete first? They group or the individual? I can see reasons for both, but I tend to side more one versus another. Curious as to how others look at it.

Now say that for the group project another person is responsible for pulling the results together and delivering however, they need to wait for your signoff before completing? Or if roles are reversed and you are the person delivering but need someone else to also complete their input and signoff - does either of these change how you prioritize (assuming you still have your own individual item to deliver as well)?