
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 observing a gathering of fifteen college students. She decides to guess whether each pair of students likes each other. Given that there's a 60% chance that any selected pair of students like each other mutually, how many pairs of students can Fiona expect to both like each other before she runs out of pairs to evaluate?

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