
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 is a checkers championship in Anchuria that consists of several rounds. The days and cities where the rounds are held are determined by a draw. According to the rules of the championship, no two rounds can take place in the same city, and no two rounds can take place on the same day. A lottery is held among the fans: the main prize is awarded to the person who correctly guesses, before the championship begins, in which cities and on which days all the rounds will take place. If no one guesses correctly, the main prize will be retained by the organizing committee. There are eight cities in Anchuria, and the championship is allocated a total of eight days. How many rounds should the championship consist of to maximize the probability that the main prize will be retained by the organizing committee?

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