
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 the vertices P, A, B, and C of the tetrahedron P-ABC are on the surface of sphere O, and triangle ABC is an equilateral triangle with a side length of $\sqrt{3}$, if the surface area of sphere O is $36\pi$, then the maximum distance from P to plane ABC is ______.

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