Points $A$, $B$, $C$, $D$, and $E$ are located on a plane. It is known that:
- $CA = 12$
- $AB = 8$
- $BC = 4$
- $CD = 5$
- $DB = 3$
- $BE = 6$
- $ED = 3$

Find the length of $AE$.

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