
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 the cabinet of ministers of Anchuria, there are 100 ministers. Among them, there are both crooks and honest ministers. It is known that among any ten ministers, at least one is a crook. What is the minimum number of crooks that could be in the cabinet?

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