
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 of 53 students registered to join one of three clubs: Science, Culture, and Lifestyle. It is required that each person must join one club and can join at most two clubs. Among all possible registration schemes, let the maximum number of people who join exactly the same set of clubs be $n$. The minimum value of $n$ is ___.

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