COUNTIFS formula to return # of dates within a specified month

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I reeeeeally tried to help myself with this one and I did come across a few other similar posts on month and date range formulas, but I keep getting invalid operation or unparseable errors with everything that I try.

Above is the start of my formula. Range 2 is a date column. How can I return the number of dates that fall within any given month?

I'm looking for a solution that avoids having to put in the first and last dates of each month.

@cell formulas haven't really clicked for me yet 😣

Any input is much appreciated!

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