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 $r$.