
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
An n-digit number has the property that if you cyclically permute its digits, the result is always divisible by 1989. What is the smallest possible value of n? What is the smallest such number?

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