(13) Let the function $f(x)=\sin x+\sqrt{3} \cos x+1$.
(1) Find the maximum and minimum values of the function $f(x)$ on $\left[0, \frac{\pi}{2}\right]$;
(2) If real numbers $a$, $b$, and $c$ satisfy $a f(x)+b f(x-c)=1$ for any $x \in \mathbf{R}$, find the value of $\frac{b \cos c}{a}$.