
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  $P$  be an interior point of a triangle  $ABC$  and let  $BP$  and  $CP$  meet  $AC$  and  $AB$  in  $E$  and  $F$  respectively. IF  $S_{BPF} = 4$ , $S_{BPC} = 8$  and  $S_{CPE} = 13$ , find  $S_{AFPE}.$ 

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