Karina L. answered 11/16/19
Experienced Writing Teacher, Applications Coach, Fulbright Recipient
I'm not sure why the carrot symbols < and > are being used here. That is not standard convention. Quotation marks should be used instead when reporting speech. If there is a quotation within a quotation, then the standard would be as follows:
Eve said, "Like my mom always said, 'Eve is the best person ever, much better than that Alice person.'"
In the example, there is a single quotation mark ' and ' inside of the standard quotation marks " and ".
I hope that helps!