3. Given $\triangle A B C, O$ is a point inside $\triangle A B C$, $\angle A O B=\angle B O C=\angle C O A=\frac{2 \pi}{3}$. Then the largest number $m$ such that
$$
A B+B C+C A \geqslant m(A O+B O+C O)
$$
holds is $(\quad$.
(A) 2
(B) $\frac{5}{3}$
(C) $\sqrt{3}$
(D) $\frac{\sqrt{3}}{2}$