Get results in a column filtered by multiple criteria

Goal:
A formula that will return the number of times a specific number appears in column Z where the agentname (column C) is "smith" and the Week Starting (column BN) has any of a range of dates in cells a3:a53(a pivot table being used as a date selector) in another worksheet named "sheet1" that is in the same workbook.

As you can see in the table on sheet1, I tried using countifs but that got me a spill error when adding in the date range requirements, so I removed it.
I thought about using Index/Match but couldn't figure out how.

Are you sure you posted the correct example? There are numbers in col Z and there are names in col C (both as noted above) but there is no range of dates in col A nor another worksheet named "X" and I don't see criteria for what you are counting.
Maybe upload another worksheet with more information AND all the extraneous columns that aren't needed for what you are asking here, you could leave out. For example your example could be three or four columns with representative examples AND expected results even if hand entered AND your sample worksheet "X" included. Any formulas we can write can simply be repointed toward your actual locations.