You can apply Early Action to a public university, but not Early Decision. REA means you can not apply anywhere else with a binding decision.
From Princeton’s Website:
Princeton University’s single-choice early action program is a nonbinding process. You may not apply to an early program at any other private college or university. However, please note the following:
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You may apply early to any public institution or service academy, as long as the decision is nonbinding.
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You may apply early to any international institution, as long as the decision is nonbinding.
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You may apply early to any college or university with a nonbinding rolling admission process.