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Is this a good path for getting accepted into Princeton or MIT?

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Hello. I'm a Sophomore in HS currently interested in pursuing a career in mathematics. The two top colleges that have caught my attention the most are Princeton and MIT. Now, the most important thing for me is not getting accepted. The most important thing to me is pursuing my interest, and becoming so filled with passion and skill and experience in it, that being accepted is merely a byproduct of that. One critical aspect that I have discovered on the matter of getting applied to an Ivy or a near-Ivy, is the pursuit and clear passion in a field, and an as close to as possible mastery of that field achieveable. I plan on expanding my passion and discovering my true interests through one of these programs. This summer, I received a letter in the mail from Brown. It was for the Pre-College Programs they were offering. Immediately, I thought what a great idea this was to get some experience. After a bit of research, a lot of which came from this forum, I learned that pre-college programs like Brown's and even Harvard's were more or less money ploys. The best that they offered, I learned, were experience. And definitely not something to consider putting on an application, especially not if the application isn't to the school with which you did the program. So, I began to look for more, focused summer programs. I learned from that research, that the best programs were ones like MOSP and RSI. Through even further research, I learned that, with no other similar experience, applying to these would not be the best for me right now, since: 1.) I would probably get rejected; 2.) It's apparently better to apply as a Junior or Senior; and 3.) The deadlines for this year have closed. Maybe I should have started with 3. No? So, I concluded that the best course of action would be to apply to go to one of the paid programs this year, for some baseline, easy experience. Then, I would go to a fairly-moderate program into which to get accepted, like PROMYS; and finally, with two more years of experience under my belt than would have been currently, I would apply to RSI. And, if I was not accept there (about which I would be disappointed), I would try for another research program like RSI. Is this a good game plan for gaining experience and knowledge in the math field? I want to know if I'm headed in the right direction. Also, I would like to take the USAMO or AIME, but I'm not sure as to when I would. I plan on taking the SAT as well. I have already taken the PSAT (1280, decent I suppose), and am taking one AP this year, and three to four next year. I am ranked #10 in my class, and I am working toward getting higher. Really just looking for some general guidance here. Any insight is greatly appreciated. Thanks for reading this far.

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