
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
Triangle  $ABC$  is equilateral with side length  $\sqrt{3}$  and circumcenter at  $O$ . Point  $P$  is in the plane such that  $(AP)(BP)(CP) = 7$ . Compute the difference between the maximum and minimum possible values of  $OP$ .

*2015 CCA Math Bonanza Team Round #8*

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