
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
Given \( n \) distinct natural numbers, any two of which can be obtained from each other by permuting the digits (the digit zero cannot be placed at the forefront). What is the largest possible value of \( n \) such that all these numbers can be divisible by the smallest of them?

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