
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
Two distinct points  $A$  and  $B$  are chosen at random from 15 points equally spaced around a circle centered at  $O$  such that each pair of points  $A$  and  $B$  has the same probability of being chosen. The probability that the perpendicular bisectors of  $OA$  and  $OB$  intersect strictly inside the circle can be expressed in the form  $\frac{m}{n}$ , where  $m,n$  are relatively prime positive integers. Find  $m+n$ .

*Ray Li.*

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