
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 appoints 9 or 10 of the 33 warriors to duty each evening at his discretion. What is the minimum number of days after which it could happen that each warrior has been on duty the same number of times?

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