
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 parabola $y^2=2px$ (where $p>0$) has its focus at point F. A line passing through F with an inclination angle of 30 degrees intersects the parabola at points A and B. The projections of points A and B on the directrix of the parabola are A′ and B′, respectively. If the area of the quadrilateral AA′B′B is 48, then the equation of the parabola is ______.

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