
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
For each of the nine natural numbers \( n, 2n, 3n, \ldots, 9n \), the first digit from the left in its decimal representation was written on the board. \( n \) was chosen so that the number of different digits among the nine written digits is as small as possible. What is this minimum number of different digits?

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