Send checkbox to range from single checkbox incrementally in Google Sheets

I have a Google Sheet with a large number of applications with multiple responses. The person going through them would like all of the information for each application formatted neatly and to give them a way to go through each application and mark whether to accept or reject the entry.

I have set up and formatted a sheet that displays all of the info from a single application with all of the answers being displayed by =Indirect() referencing a hidden value. A simple next button attached to a script increases that value by 1 to bring up the next application.

I need a way to send the Accept/Reject value back to the first sheets raw data, but it seems like checkboxes only work with formulas when they are receiving a value. Because the same cell is being used when parsing through applications, I have no way of referencing that checkbox in the raw data.

I think I need to have a script check the indirect value to know which application is currently being used and then send TRUE to the correct cell, then have it be reset back to unchecked (potentially as part of the 'Next' button)?

Hopefully I explained this well enough and thanks for any help~