14. Given the function $f(x)=\frac{x^{3}+3 x}{3 x^{2}+1}$, the sequence $\left\{x_{n}\right\}$ satisfies $x_{1}=2, x_{n+1}=f\left(x_{n}\right)\left(n \in \mathbf{N}_{+}\right)$.
Let $b_{n}=\log _{3}\left(\frac{x_{n+1}-1}{x_{n+1}+1}\right)\left(n \in \mathbf{N}_{+}\right)$.
(1) Prove that $\left\{b_{n}\right\}$ is a geometric sequence, and find the general term formula for the sequence $\left\{b_{n}\right\}$;
(2) Let $c_{n}=-n b_{n}\left(n \in \mathbf{N}_{+}\right)$, find the sum of the first $n$ terms of the sequence $\left\{c_{n}\right\}$, denoted as $T_{n}$.