Example 6 Function $f$ is defined on the set of real numbers, and for all real numbers $x$ it satisfies the equations
$f(2-x)=f(2+x)$ and $f(7-x)=f(7+x)$. Suppose $x=0$ is a root of $f(x)=0$, and let $N$ be the number of roots of $f(x)=0$ in the interval $[-1000,1000]$. Find the minimum value of $N$.