Two Equilateral Triangles and a Moving Point

In equilateral triangle $ABC$, $D$ and $E$ are the midpoints of $AB$ and $AC$ respectively. $M$ is a moving point on ray $BC$. On the side of line $DM$ opposite to $B$, an equilateral triangle $DMN$ is constructed. Determine the positional relationship between $EN$ and $AB$, and prove it.