
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 an isosceles triangle \( \triangle ABC \) with \( AB = AC = \sqrt{5} \), point \( D \) is on side \( BC \) but not the midpoint. Point \( E \) is the reflection of point \( C \) about 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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