A group of 6 students decided to form "study groups" and "service activity groups" based on the following principle:

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

Given that there is at least one group and no three students belong to both the same study group and service activity group, find the minimum number of groups.

Let's think step by step and output the final answer within \boxed{}.
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