
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
Given a parabola $y^2 = 2px$, where a straight line $l$ passes through its focus and is perpendicular to the x-axis, intersecting the parabola at points A and B. If $|AB| = 10$ and P is a point on the directrix of the parabola, calculate the area of the triangle $\triangle ABP$.

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