
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
There are representants from  $n$  different countries sit around a circular table ( $n\geq2$ ), in such way that if two representants are from the same country, then, their neighbors to the right are not from the same country. Find, for every  $n$ , the maximal number of people that can be sit around the table.

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