
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
The side \( AB \) of triangle \( ABC \) is equal to 3, \( BC = 2AC \), \( E \) is the point of intersection of the extension of the angle bisector \( CD \) of this triangle with the circumscribed circle around it, \( DE = 1 \). Find \( AC \).

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