
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 focus of the parabola $y^2=4x$ is $F$, and its directrix $l$ intersects the x-axis at point $E$. A line passing through $F$ with an inclination angle of $60^\circ$ intersects the upper part of the parabola at point $A$, where $AB \perp l$ and the foot of the perpendicular is $B$. Calculate the area of quadrilateral $ABEF$.

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