(3) In $\triangle A B C$, the angle between $\overrightarrow{A B}$ and $\overrightarrow{B C}$ is $150^{\circ},|\overrightarrow{A C}|=2$, then the range of $|\overrightarrow{A B}|$ is $\qquad$ .
(3) $(0,4]$ Hint: Since the angle between $\overrightarrow{A B}$ and $\overrightarrow{B C}$ is $150^{\circ}$, $\angle B=30^{\circ}$. By the Law of Sines, $\frac{|\overrightarrow{A B}|}{\sin C}=\frac{|\overrightarrow{A C}|}{\sin 30^{\circ}}=4$, so $|\overrightarrow{A B}|=4 \sin C$. Since $0^{\circ}<\angle C<150^{\circ}$, the range of $|\overrightarrow{A B}|$ is $(0,4]$.