
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 of radius $\sqrt{3}$ and a side of an equilateral triangle $ABC$. The circle also intersects $AC$ and $BC$ at points $D$ and $E$, respectively. Calculate the length of $AE$.
A) $2\sqrt{3}$
B) $3\sqrt{2}$
C) $3$
D) $4$
E) $5$

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