
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  $ABCD$  be a parallelogram with area 160. Let diagonals  $AC$  and  $BD$  intersect at  $E$ . Point  $P$  is on  $\overline{AE}$  such that  $EC = 4EP$ . If line  $DP$  intersects  $AB$  at  $F$ , find the area of  $BFPC$ .

*Proposed by Andy Xu*

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