You and a buddy start with a rectangular cake, represented by rectangle $ABCD$ in Figure 1. Then you get to pick any point $E$ between $C$ and $D$, and the cake is sliced with two straight cuts, from $B$ to $E$ and $E$ to $A$. Then it’s your friend’s turn to pick a point $F$ between $B$ and $C$, so that the cake will be sliced from $D$ to $F$ and $F$ to $A$. The four straight slices intersect at points $G$, $H$, and $I$ as shown in Figure 1. You receive piece $AGHI$ of the cake, and the other player receives pieces $DEG$, $CEHF$, and $BFI$.

Determine all points $E$ you can choose on side $CD$ that will prevent your buddy from ending up with more cake (in all) than you do.