Of the schools on your list, Harvard, Yale and Princeton offer the so-called single-choice/restrictive early action (SCEA/REA). If you SCEA/REA to one of these schools, then you may not ED/EA to any other private school (EAing to public schools such as Michigan is fine). If, instead, you ED to Cornell as stated, then you may EA to all schools on your list that offer EA but not SCEA/REA. In fact, there is no downside to choosing EA over RD, unless you need more time to finish your essays.
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