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

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

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

![](https://cdn.mathpix.com/cropped/2024_05_06_d4986512fdb0330805a0g-23.jpg?height=404&width=293&top_left_y=93&top_left_x=580)

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