
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
In $\triangle ABC$, $D$ is on segment $AC$ such that $AD = DC = x$, and $E$ is on segment $BC$. Furthermore, $AB \perp AC$, $AE \perp BC$, and $DE = EC = 2$. Determine the length of $AC$.
A) $1 + \sqrt{17}$
B) $\sqrt{15}$
C) $\sqrt{13}$
D) $2 + \sqrt{17}$
E) $\sqrt{17}$

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