
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 the diagram, $\triangle ABE$, $\triangle BCE$ and $\triangle CDE$ are in a configuration where $\triangle ABE$ and $\triangle BCE$ are right-angled at $E$ with $\angle AEB = \angle BEC = 60^\circ$ and $\triangle CDE$ is an equilateral triangle. Given that $AE = 20\sqrt{3}$, find the perimeter of quadrilateral $ABCD$.

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