
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
Around a circle are written the natural numbers from 1 to \( N \) with \( N > 2 \), such that each number is written only once and each pair of neighboring numbers has at least one digit in common. Find the smallest \( N > 2 \) for which this is possible.

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