
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 tennis tournament there are participants from  $n$  different countries. Each team consists of a coach and a player whom should settle in a hotel. The rooms considered for the settlement of coaches are different from players' ones. Each player wants to be in a room whose roommates are **<u>all</u>** from countries which have a defense agreement with the player's country. Conversely, each coach wants to be in a room whose roommates are **<u>all</u>** from countries which don't have a defense agreement with the coach's country. Find the minimum number of the rooms such that we can <u>**always**</u> grant everyone's desire.

*proposed by Seyed Reza Hosseini and Mohammad Amin Ghiasi*

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