Academics are just one component of admission to the top tier colleges (and I agree with @momofsenior1 about re-taking the ACT if you think you can raise your score). There are many other factors such as: recommendations, essays, ECs, what a college is looking for to fill its class etc. that go into admission decisions. Those schools must be considered to be reaches for any unhooked applicant.
Princeton’s acceptance rate is 7%. so the answer is “unlikely”, before even looking at your scores/grades.
ACT 32 is the bottom end of Princeton’s 25%-75% ACT scores for admitted students. Available data says most admitted students have between 7 and 12 AP courses, though it’s dependent on what the high school made available.
I would agree with your classification that it’s a reach, given the data provided.
"Academics are just one component of admission to the top tier colleges "
While this is true, it’s often used to imply “don’t worry, you can make up for low grades and low test scores with other things.”
GPA and Test Scores are by far the most heavily weighted part of an admission decision. A great essay and two awesome recommendations almost certainly make a dent in a 3.5 and 1400 applying to any Ivy League school…