
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
Fiona is at a large social gathering where the number of high schoolers ranges between 10 and 15. She continues her game of guessing relationships within each pair of people she observes. What is the minimum and maximum number of pairs of high schoolers she can observe before she runs out of pairs to evaluate?

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