
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
The digits 1 and 2 are arranged in a circle. A "depicted" number is a number formed by several consecutive digits (in a clockwise or counterclockwise direction). What is the smallest value of $N$ for which all four-digit numbers, containing only the digits 1 and 2, can be among the depicted?

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