(9) In $\triangle A B C$, the lengths of the sides opposite to angles $A, B, C$ are $a, b, c$ respectively. It is known that $a^{2}, b^{2}, c^{2}$ form an arithmetic sequence.
(1) Find the range of $B$;
(2) If the equation $\sqrt{3} \cos B+\sin B=m$ has exactly one solution for $B$, find the value of the real number $m$.
(9) (1) Since $a^{2}, b^{2}, c^{2}$ form an arithmetic sequence, we have $2 b^{2}=a^{2}+c^{2}$. Therefore,
$$
\cos B=\frac{a^{2}+c^{2}-b^{2}}{2 a c}=\frac{a^{2}+c^{2}}{4 a c} \geqslant \frac{2 a c}{4 a c}=\frac{1}{2}.
$$

Since $0<B<\pi$, the range of angle $B$ is $\left(0, \frac{\pi}{3}\right]$.
(2) It is easy to see that $\sqrt{3} \cos B+\sin B=2 \sin \left(B+\frac{\pi}{3}\right)$.
From (1), we know $\frac{\pi}{3}<B+\frac{\pi}{3} \leqslant \frac{2 \pi}{3}$, so $m=2$ or $\sqrt{3}$.