
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
Let  $ABC$  be a triangle with  $AB = 3$ ,  $BC = 4$ , and  $AC =5$ . If  $D$  is the projection from  $B$  onto  $AC$ ,  $E$  is the projection from  $D$  onto  $BC$ , and  $F$  is the projection from  $E$  onto  $AC$ , compute the length of the segment  $DF$ .

*2016 CCA Math Bonanza Individual #5*

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