13. Given $\triangle A B C$ with internal angles $\angle A, \angle B, \angle C$ and their opposite sides $a, b, c$ respectively, and it is known that $1+\frac{\tan B}{\tan A}=\frac{2 c}{\sqrt{3} a}$.
(1) Find $\angle B$;
(2) If $\triangle A B C$ is an acute triangle, and $a=2$, find the range of the area of $\triangle A B C$.