
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 set of five-digit numbers \(\left\{N_{1}, N_{k}\right\}\) is such that any five-digit number, with digits in non-decreasing order, has at least one digit in common with at least one of the numbers \(N_{1}, N_{k}\). Find the smallest possible value of \(k\).

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