13. (15 points) In $\triangle A B C$, $a$, $b$, and $c$ are the sides opposite to $\angle A$, $\angle B$, and $\angle C$ respectively, with $b=1$, and 
$\cos C+(2 a+c) \cos B=0$.
Find (1) $\angle B$;
(2) the maximum value of $S_{\triangle A B C}$.
Three, 13. (1) From the given information,
$$
\begin{array}{l}
b \cos C+(2 a+c) \cos B=0 \\
\Rightarrow \sin B \cdot \cos C+(2 \sin A+\sin C) \cos B=0 \\
\Rightarrow \sin (B+C)+2 \sin A \cdot \cos B=0 \\
\Rightarrow \sin A+2 \sin A \cdot \cos B=0 .
\end{array}
$$

Since $\angle A, \angle B$ are the interior angles of $\triangle ABC$, we have $\cos B=-\frac{1}{2} \Rightarrow \angle B=\frac{2 \pi}{3}$.
(2) Substituting $b=1, \angle B=\frac{2 \pi}{3}$ into
$$
b^{2}=a^{2}+c^{2}-2 a c \cos B
$$

we get $\quad 1=a^{2}+c^{2}+a c \geqslant 3 a c \Rightarrow a c \leqslant \frac{1}{3}$
$\Rightarrow S_{\triangle A B C}=\frac{1}{2} a c \sin B \leqslant \frac{1}{2} \times \frac{1}{3} \sin \frac{2 \pi}{3}=\frac{\sqrt{3}}{12}$.
When $\angle B=\frac{2 \pi}{3}, \angle A=\angle C=\frac{\pi}{6}$, $S_{\triangle A B C}$ reaches its maximum value.