Using the Supplemental information is advised when dealing with RSU sales. The Supplemental information contains the cost basis that you need to adjust for the sale, and usually that basis is not reported properly on the Form 1099-B.
Using the same logic, going with the Supplemental information purchase date makes sense. However, make sure that you are matching the Supplemental RSU sales with the sales listed on the Form 1099-B to ensure you are picking up the correct basis for each sale.
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