4. As shown in Figure $14-13, A C$ and $C E$ are two diagonals of the regular hexagon $A B C D E F$. Points $M$ and $N$ internally divide $A C$ and $C E$ respectively, such that $A M: A C = C N: C E = r$. If points $B$, $M$, and $N$ are collinear, find the value of $r$.

保留源文本的换行和格式如下：

4. As shown in Figure $14-13, A C$ and $C E$ are two diagonals of the regular hexagon $A B C D E F$. Points $M$ and $N$ internally divide $A C$ and $C E$ respectively, such that $A M: A C = C N: C E = r$. If points $B$, $M$, and $N$ are collinear, find the value of $r$.
4. Connect $B D, N D$. Since $\triangle M B C$ rotates counterclockwise by $120^{\circ}$ around point $O$ and coincides with $\triangle N D E$, we know that $\angle B N D=120^{\circ}$. Construct an equilateral triangle $B D G$ on the other side of point $N$ with $B D$ as one side, then points $N, B, G, D$ are concyclic and $C$ is the center of this circle. Therefore, $C N=C B$. Hence
$$
r=C N: C E=C B: C E=\frac{\sqrt{3}}{3} \text {. }
$$