Firstly you need to make sure that the Add Assignment action is not an "Optional Action" on the status. And then the Add Assignment action needs to be brought into the process so that it is visible as a light blue coloured manual action.^
Then you place an Add Reminder action as a green automatic action after it, then loop from the Reminder back into the status that this action was performed on.
Difficult to put into words what I mean. I would highly reccomend having a read from page 166 onwards on the designer guide which will give a full walk through of adding an automatic notification to a process. The example seen in the guide is for Add Note, but the same principle can be applied for Add Assignment,
The most current version of document is for 7.8.3 and can be found here LANDESK Service Desk 7.8.3 - Designer Guide
For earlier versions of the document and other manuals check here Ivanti Service Desk and Asset Manager Landing Page
I hope that will give you the information that you need.
Truly I cannot thank you enough. I am so very grateful for your kindness. Your help allows me to learn more each time about LANDesk Service Desk. Thank you, so very much.