
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
An isosceles triangle \( ABC \) is given (\( AB = BC \)). On the ray \( BA \) beyond the point \( A \), point \( E \) is marked, and on the side \( BC \), point \( D \) is marked. It is known that

\[
\angle ADC = \angle AEC = 60^\circ, \quad AD = CE = 13.
\]

Find the length of segment \( AE \), if \( DC = 9 \).

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