
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 three rays, $PA$, $PB$, and $PC$, depart from point $P$ and form a $60^{\circ}$ angle with each other. They are tangent to sphere $O$ at points $A$, $B$, and $C$ respectively. If the volume of sphere $O$ is $36π$, find the distance between points $O$ and $P$.

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