
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
Karel drew triangle \( A D E \). On side \( A D \), he marked points \( B \) and \( C \) such that:

- Point \( C \) is the midpoint of side \( A D \),
- Triangles \( A B E \) and \( B C E \) have the same area,
- Triangle \( B D E \) is isosceles with base \( B E \),
- The perimeter of triangle \( A B E \) is \( 6 \) cm greater than the length of the broken line \( E B C \),
- The perimeter of triangle \( A C E \) is \( 2 \) cm greater than the perimeter of triangle \( C D E \).

Calculate the perimeter of triangle \( A D E \).

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