
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 area of trapezoid \(ABCD\) is 6. Let \(E\) be the intersection point of the extensions of the non-parallel sides of this trapezoid. A line is drawn through \(E\) and the intersection point of the diagonals of the trapezoid, intersecting the shorter base \(BC\) at point \(P\) and the longer base \(AD\) at point \(Q\). Point \(F\) lies on segment \(EC\), such that \(EF: FC = EP: EQ = 1:3\). Find the area of triangle \(EPF\).

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