
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
Wendy takes Honors Biology at school, a smallish class with only fourteen students (including Wendy) who sit around a circular table.  Wendy's friends Lucy, Starling, and Erin are also in that class.  Last Monday none of the fourteen students were absent from class.  Before the teacher arrived, Lucy and Starling stretched out a blue piece of yarn between them.  Then Wendy and Erin stretched out a red piece of yarn between them at about the same height so that the yarn would intersect if possible.  If all possible positions of the students around the table are equally likely, let  $m/n$  be the probability that the yarns intersect, where  $m$  and  $n$  are relatively prime positive integers.  Compute  $m+n$ .

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