
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 the isosceles $\triangle ABC$, $AB = AC = \sqrt{5}$, $D$ is a point on side $BC$ that is not the midpoint, and $E$ is the symmetric point of $C$ with respect to line $AD$. The extension of $EB$ intersects the extension of $AD$ at point $F$. Find the value of $AD \cdot AF$.

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