
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
A line passing through the focus F of the parabola $y^2=2px$ ($p>0$) is parallel to one of the asymptotes of the hyperbola $x^2-\frac{y^2}{8}=1$ and intersects the parabola at points A and B. If $|AF| > |BF|$ and $|AF|=3$, find the equation of the parabola.

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