
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
Circle $O$ has a radius of 2, and segment $AB$ serves as both a diameter and a hypotenuse of a right triangle $ABC$ where $\angle ACB = 90^\circ$ and $\angle ABC = 60^\circ$. Define $D$ as the intersection of circle $O$ and segment $AC$, and $E$ as the intersection of circle $O$ and segment $BC$. Calculate the length of segment $AE$.
A) 1
B) $\sqrt{2}$
C) 2
D) $\sqrt{3}$
E) 4

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