I am looking to create a multi-function formula- Count when the course is X or X AND status complete

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I am summerizing data for a dashboard in a secondary sheet and need to find if two courses of many are selected AND the status is complete. I have the column before with the counting of the two courses and need to add on the completion status either by referencing the previous column or in a formula by itself and even after reviewing all the similar questions and help articles, I can't seem to get it to work:

This formula works for the previous column- =COUNTIF({xxx 2022 data input sheet Range 1}, "Course X") + COUNTIF({xxx 2022 data input sheet Range 1}, "Course Y")

Can't seem to add the additional criteria?

=COUNTIFS({xxx 2022 data input sheet Range 1}, "course x") + COUNTIFS({xxx 2022 data input sheet Range 1}, "course y") OR(COUNTIF({xxx 2022 data input sheet Range 3}, "Complete")

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