设数列 $\left\{x_{n}\right\}$ 满足 $0 < x_{1} < \pi, x_{n+1}=\sin x_{n}(n=1,2, \cdots)$.
(I) 证明 $\lim _{n \rightarrow \infty} x_{n}$ 存在, 并求该极限;
(II) 计算 $\lim _{n \rightarrow \infty}\left(\frac{x_{n+1}}{x_{n}}\right)^{\frac{1}{x_{n}^{2}}}$.
$\text{A.}$
$\text{B.}$
$\text{C.}$
$\text{D.}$