In the figure below, $ABCD$ is a rectangle and $E$ is the midpoint of $AD$. The segment $FG$ passes through the midpoint $M$ of $CE$. Determine the ratio between the lengths of $GM$ and $MF$.

![](https://cdn.mathpix.com/cropped/2024_05_01_360f8ce7ec440aed2c7ag-16.jpg?height=351&width=580&top_left_y=1115&top_left_x=652)