
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
Segment $AB$ is both a diameter of a circle with radius $2$ and a side of an equilateral triangle $ABC$. The circle also intersects $AC$ and $BC$ at points $D$ and $E$, respectively. What is the length of $AE$?
A) $4$
B) $2\sqrt{3}$
C) $\sqrt{3}$
D) $1.5\sqrt{3}$
E) $8$

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