
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 that point A is on the parabola $C: x^2 = 2py$ ($p>0$), and O is the origin. If A and B are two points on the parabola $C$ that, along with point M(0, 9), form a circle with the radius equal to the length of $|OA|$, and $\triangle ABO$ is an equilateral triangle, then the value of $p$ is \_\_\_\_\_\_.

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