Define a sequence recursively by $x_0=3$ and $x_{n+1}=\frac{x_n^2+3x_n+2}{x_n+4}$ for all nonnegative integers $n$. Let $m$ be the least positive integer such that $x_m\le 2+\frac{1}{2^{25}}$. In which of the following intervals does $m$ lie?