
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
Consider a prime number \( p \). We need to design a Parchís tournament subject to the following rules:

- The tournament involves \( p^{2} \) players.
- In each game, \( p \) players participate.
- The tournament is divided into rounds. Each round is divided into games. Each player plays one, or no, game in each round.
- At the end of the tournament, each player has played exactly once against every other player.

Determine whether it is possible to design such a tournament. If yes, find the minimum number of rounds the tournament can have.

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