
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 group of 6 students decided to make *study groups* and *service activity groups* according to the following principle:

Each group must have exactly 3 members. For any pair of students, there are same number of study groups and service activity groups that both of the students are members.

Supposing there are at least one group and no three students belong to the same study group and service activity group, find the minimum number of groups.

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