chance me applied math, public exam school, looking at MIT / Caltech / Princeton

Demographics: - female - NYC public exam school (Stuyvesant) - middle income - no hooks Intended major: Applied Math + Econ double, Wharton M&T as the cross-admit dream Academics: - GPA: 3.97 UW / 4.62 W - SAT: 1560 - 12 APs through senior fall (Calc BC 5, Stats 5, Macro 5, Micro 5) ECs: - AIME qualifier 2x, AMC 12 distinguished honor roll - Stuy math team, ARML team representative - Tutoring at the Stuy peer-tutoring center, ~100 hours over two years - Internship at a Manhattan quant fund summer between junior and senior year (data analysis intern, real desk exposure) - Stuy econ club, organized two industry speaker events Awards: - AIME qualifier 2x - NYS Math League individual all-state - AP Scholar with Distinction - Stuy faculty math award (junior year) Schools: Reach: - MIT - Caltech - Princeton (ORFE) - Harvard - Penn (Wharton M&T as the absolute dream cross-admit) Match: - Cornell - UMich - Northwestern (MMSS) - UC Berkeley Safety: - Stony Brook - Binghamton - CUNY Macaulay am i out of my mind for putting MIT and Caltech both as reaches when AIME is the strongest thing on my app. is that enough or do i need to lean harder on the quant internship in essays. be honest