9、(16 points) In the sequence $\left\{a_{n}\right\}$, it is known that $a_{1}=1, a_{2}=\frac{1}{4}$, and $a_{n+1}=\frac{(n-1) a_{n}}{n-a_{n}}(n=2,3, \cdots)$  
(1) Find the general term formula of the sequence $\left\{a_{n}\right\}$  
(2) Prove: For all $n \in \mathbb{N}^{*}$, $\sum_{k=1}^{n} a_{k}^{2}<\frac{7}{6}$.