
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
Uncle Chernomor assigns 9 or 10 of his thirty-three bogatyrs to duty every evening. What is the minimum number of days required so that all the bogatyrs have been on duty the same number of times?

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