
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
In the right-angled triangle $AOB$, all three vertices lie on the parabola $y^2=2px$, where the right-angle vertex $O$ is at the origin, and the line containing $OA$ has the equation $y=\sqrt{3}x$. The area of $\Delta AOB$ is $6\sqrt{3}$. Find the equation of this parabola.

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