One. (15 points) As shown in Figure 1, $A$ is a fixed point between two parallel lines $l_{1}$ and $l_{2}$, and the distances from point $A$ to lines $l_{1}$ and $l_{2}$ are $A M=1, A N=\sqrt{3}$. Let the other two vertices $C$ and $B$ of $\triangle A B C$ move on $l_{1}$ and $l_{2}$ respectively, and satisfy $A B<A C, \frac{A B}{\cos B}=\frac{A C}{\cos C}$.
(1) Determine the shape of $\triangle A B C$ and prove the conclusion;
(2) Find the maximum value of $\frac{1}{A B}+\frac{\sqrt{3}}{A C}$.