
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
Given a natural number \( k \). In a city, there are several children who attend several clubs. It is known that no more than \( 3k \) children attend each club, any child attends exactly three clubs, and for any two children, there is a club that both of them attend. What is the maximum number of children that can be in the city?

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