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Viertel has been a member of the institution's board for almost three decades and its chairman since 2000.
She points out that now is the time for "new, fresh, innovative work" on Broadway.
The versatile actor just picked up her eighth Tony nomination for the now-closed Days of Wine and Roses.
Jack O'Brien will direct Jen Silverman's comedy.
For each of these three women, the musical marks a personal milestone.
Rob Ruggiero will direct the classic musical by Joseph Stein, Jerry Bock, and Sheldon Harnick.
In the piece, Nathan Queeley-Dennis takes audiences on a sensitive and revealing journey through dating.
Hannah Khalique-Brown will be Mary Lennox in Holly Robinson and Anna Himali Howard's new play.
Originally a production of the York Theatre Company, the musical will play its final performance at New World Stages in June.