
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
The three points \( A, B, C \) form a triangle. \( AB = 4 \), \( BC = 5 \), \( AC = 6 \). Let the angle bisector of \(\angle A\) intersect side \(BC\) at \(D\). Let the foot of the perpendicular from \(B\) to the angle bisector of \(\angle A\) be \(E\). Let the line through \(E\) parallel to \(AC\) meet \(BC\) at \(F\). Compute \(DF\).

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