You will probably have to deactive the process first. Then open that status and highlight the "add assignment" action and go to the properties of it. within there you can add more details into the description.
Thanks for your sugesstion, but this not solved my problem...
On "assignment prop.jpg" is what I can choose when assignment is choosen,
On "in progress state prop.jpg" is what I see when In Progress is doubleclicked, and optional action is choosen.
Process is now deactivated.
If you have trouble with it being stored in the process you could always remove it as an option within the process and drag the add assignment into the workflow and connect it to in progress. This may give you the result you are looking for.
What version are you running?
With separate step in the process, assignment messages looks like I want
My version is 7.5 SP1