
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 company has $n$ employees. It is known that for every pair of these $n$ employees, it can be guaranteed that there are at least three days in a week when one of the employees is working while the other is not (these days do not necessarily involve the same employee working, and employees may choose not to work at all during the week). Determine the maximum value of $n$.

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