
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
In a certain meeting, there are 30 participants. Each person knows at most 5 others among the remaining participants, and in any group of 5 people, there are always two who do not know each other. Find the largest positive integer \( k \) such that there exists a subset of \( k \) people from these 30 people who do not know each other.

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