
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
An isosceles trapezoid \(ABCD\) is inscribed in a circle with radius \(2 \sqrt{7}\), whereby its base \(AD\) is the diameter, and angle \(\angle BAD\) is \(60^\circ\). Chord \(CE\) intersects the diameter \(AD\) at point \(P\) such that the ratio \(AP:PD = 1:3\). Find the area of triangle \(BPE\).

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