18. Given vectors $\boldsymbol{m}=(\sin A, \cos A), \boldsymbol{n}=(\cos B, \sin B), \boldsymbol{m} \cdot \boldsymbol{n}=\sin 2 C$, and $A, B, C$ are the angles opposite to sides $a, b, c$ of $\triangle A B C$.
(1) Find the size of $C$;
(2) If $\sin A, \sin C, \sin B$ form a geometric sequence, and $\overrightarrow{C A} \cdot \overrightarrow{C B}=18$, find the value of $c$.
(1) $\sin A \cos B+\cos A \sin B=\sin (A+B)=\sin C=\sin 2 C \Rightarrow \cos C=\frac{1}{2} \Rightarrow C=60^{\circ}$.
(2) $\sin A \cdot \sin B=\sin ^{2} C, a b \cos C=18 \Rightarrow a b=36$, by the Law of Sines we get $c^{2}=a b=36 \Rightarrow c=6$.