In $\triangle ABC$ with a right angle at $C$, point $D$ lies in the interior of $\overline{AB}$ and point $E$ lies in the interior of $\overline{BC}$ so that $AC=CD,$ $DE=EB,$ and the ratio $AC:DE=4:3$. The original answer is in the form x:y for the ratio $AD:DB$. Please give the value of x + y.

Let's think step by step and output the final answer within \boxed{}.
user