Nemotron-IMO-Bench 2026 A11

Is there a sequence of pairs of real numbers $(x_n, y_n)_{n\geq 1}$ such that for any sequence $(b_n)_{n\geq 1}$ of real numbers there is a polynomial $f\in \mathbb{R}[X,Y]$ with $f(x_n, y_n)=b_n$ for all $n$?