
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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