
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
Line segment \(AB\) is both the diameter of a circle with radius 1 and a side of an equilateral triangle \(\triangle ABC\). The circle intersects \(AC\) and \(BC\) at points \(D\) and \(E\), respectively. Calculate the length of \(AE\).

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