
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
Points \( D \) and \( E \) are marked on the sides \( AC \) and \( BC \) of triangle \( ABC \) respectively, such that \( AD = EC \). It is known that \( BD = ED \) and \(\angle BDC = \angle DEB\). Find the length of segment \( AC \) given that \( AB = 7 \) and \( BE = 2 \).

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