
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 each of the employees works at least one of the  $7$  days of the week, with the exception of an employee who does not work any of the  $7$  days. Furthermore, for any two of these  $n$  employees, there are at least  $3$  days of the week in which one of the two works that day and the other does not (it is not necessarily the same employee who works those days). Determine the highest possible value of  $n$ .

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