
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 turns out that $BD = ED$ and $\angle BDC = \angle DEB$. Find the length of the segment $AC$, given that $AB = 7$ and $BE = 2$.

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