US-TST 2020 Problem 1

Choose positive integers $b_{1}, b_{2}, \ldots$ satisfying $$1=\frac{b_{1}}{1^{2}}>\frac{b_{2}}{2^{2}}>\frac{b_{3}}{3^{2}}>\frac{b_{4}}{4^{2}}>\cdots$$ and let $r$ denote the largest real number satisfying $\frac{b_{n}}{n^{2}} \geq r$ for all positive integers $n$. What are the possible values of $r$ across all possible choices of the sequence $\left(b_{n}\right)$ ?