27. Given $f(x)=\frac{1}{\sqrt{x^{2}-4}}(x>2), f^{-1}(x)$ is its inverse function.
(1) If the sequence $\left\{a_{n}\right\}$ satisfies $a_{1}=1, a_{n+1}=\frac{1}{f^{-1}\left(a_{n}\right)}$, find $\left\{a_{n}\right\}$;
(2) Let $S_{n}=a_{1}^{2}+a_{2}^{2}+\cdots+a_{n}^{2}, b_{n}=S_{2 n+1}-S_{n}$, does there exist a largest positive integer $p$, such that for all $n$, $b_{n}<\frac{1}{p}$ holds?