13. Given the sequence $\left\{a_{n}\right\}$ satisfies:
$$
a_{1}=a, a_{n+1}=\frac{5 a_{n}-8}{a_{n}-1}\left(n \in \mathbf{Z}_{+}\right) .
$$
(1) If $a=3$, prove that $\left\{\frac{a_{n}-2}{a_{n}-4}\right\}$ is a geometric sequence, and find the general term formula of the sequence $\left\{a_{n}\right\}$;
(2) If for any positive integer $n$, $a_{n}>3$, find the range of the real number $a$.