KöMaL 2024 C1819

Let $ABCD$ be a unit square, and let $k$ be the circle with center $A$ and radius $AC$. Let $E$ and $F$ be the points of intersection of circle $k$ and rays $AB$ and $AD$, respectively. Let line $EF$ intersect $BC$ at point $G$, and let $H$ be the reflection of point $B$ across line $AG$. Find the length of line segment $HE$ in the given unit.