
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  $30$  students such that each student has at most  $5$  friends and for every  $5$  students there is a pair of students that are not friends, determine the maximum  $k$  such that for all such possible configurations, there exists  $k$  students who are all not friends.

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