
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 Anchuria, a checkers championship takes place over several rounds. The days and cities for hosting the rounds are determined by a draw. According to the championship rules, no two rounds can be held in the same city and no two rounds can be held on the same day. A lottery is held among the fans: the grand prize goes to the person who correctly guesses the cities and days for all the rounds before the championship starts. If no one guesses correctly, the grand prize is awarded to the championship organizing committee. There are eight cities in Anchuria, and the championship is scheduled to take place over eight days. How many rounds should there be in the championship to maximize the probability that the organizing committee wins the grand prize?

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