While this can be done with Actions, I suggest using formuals will be an easier setup.
You can have a summary field to count the # of reports which are completed. The have a field on the Project called [Checkbox Status] to show as a calculated checkbox
[# of reports completed] > 0 or [Project checkmark]=true
Then on the child record, similarly you can lookup [Checkbox Status] to the Reports table and have a formula field called [Report Status] like
[checkbox status lookup] = true or [Reports checkbox] = true
