
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
In convex quadrilateral $ABCD$, sides $AB = 8$ and $CD = 16$ meet at angle $A$ which is $60^\circ$, diagonals $AC$ and $BD$ intersect at $E$, $AC = 20$, and the areas of $\triangle AEB$ and $\triangle CED$ are equal. Find the length of $AE$.
A) $8$
B) $10$
C) $12$
D) $16$
E) $20$

Present the answer in LaTex format: \boxed{Your answer}
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