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Alexander's first professional performance was on stage at the age of 11 in New York City at the Public Theater in the musical Bloody Bloody Andrew Jackson. He then went on to perform in the Broadway national tour of Billy Elliot the Musical. He has had several episodic roles on television. His first film role was in 2013's summer indie hit The Way, Way Back in the role of Peter. He was also in Boychoir, which was released in 2015.