10. (20 points) In the sequence $\left\{a_{n}\right\}$,
$$
\begin{array}{l}
a_{1}=1, \\
a_{n}=\frac{n}{n-1} a_{n-1}+2 n \times 3^{n-2}(n \in \mathbf{N}, n \geqslant 2) .
\end{array}
$$
(1) Find the general term $a_{n}$;
(2) Let $b_{n}=\frac{a_{n+1}}{n+1}\left(n \in \mathbf{Z}_{+}\right)$, prove: The sum of the first $n$ terms of the sequence $\left\{\frac{2 b_{n}}{\left(b_{n}-1\right)^{2}}\right\}$ is $S_{n}<2$.