9. (14 points) Let $\triangle A B C$ have $\angle A, \angle B, \angle C$ opposite sides $a, b, c$ respectively, and $2 a \cos C=2 b-c$. Find
(1) the size of $\angle A$;
(2) the range of $b+c$ when $a=1$.

保留源文本的换行和格式，直接输出翻译结果。
9. (1) From $2 a \cos C=2 b-c$, we get
$$
\begin{array}{l}
\sin A \cdot \cos C+\frac{1}{2} \sin C=\sin B \\
=\sin (A+C)=\sin A \cdot \cos C+\cos A \cdot \sin C \\
\text { then } \frac{1}{2} \sin C=\cos A \cdot \sin C \text {. }
\end{array}
$$

Since $\sin C \neq 0$, thus, $\cos A=\frac{1}{2}$.
Also, $0a=1$, hence the range of $b+c$ is $(1,2]$.