
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 chess tournament is organized with the following system: each of the 15 students from the "White Rook" school must play once against each of the 20 students from the "Black Elephant" school, making a total of 300 games. At any moment, no more than one game is played.

After \( n \) games, a fan named Sasha, who watched all the games and knows all the participants, exclaimed: "I can definitely name one of the participants in the next game!" What is the minimum \( n \) for this to happen?

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