
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 class plans to arrange some students to participate in activities over a week (6 days). Each day, a certain number of students are arranged, but among the students who participate in any three days, there must be at least one student who participates in all three days. However, among the students who participate in any four days, there must be no student who participates in all four days. What is the minimum number of students in this class, and how can they be specifically arranged to meet the conditions?

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