Example 2. Add a figure, in $\triangle A B C$, $D, E$ are the trisection points on $B C$, point $M$ is the midpoint of $A C$, $B M$ intersects $A D$ at $G$,
intersects $A E$ at $H$. Then
$$
\begin{array}{l}
B G: G H: H M \\
=(\quad) .
\end{array}
$$
(A) $3: 2: 1$
(B) $4: 2: 1$
(C) $5:$
(D) $5: 3: 2$