
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
A local high school math club has 12 students in it. Each week, 6 of the students go on a field trip.
(a) Jeffrey, a student in the math club, has been on a trip with each other student in the math club. Determine the minimum number of trips that Jeffrey could have gone on.
(b) If each pair of students have been on at least one field trip together, determine the minimum number of field trips that could have happened.

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