Trouble with nested IF-COUNTIF Formula

I am new to COUNTIF formulas. I am trying to write a nested COUNTIF statement for Column J

If the answer in Column E is “False”, then “NA” in Column J,
But, if the answer in Column E is “True”, and there is a “Y” in any one of the columns F through I, then “PRCS”, otherwise “NPRCS”

I have tried many different combinations of Ifs and COUNTIF(F6:I6,”Y”)>=1 with no success…

I have attached a sample spreadsheet with relevant cells.

Help would be greatly appreciated.