
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  $9$  positive integers  $n,2n,3n,\dots , 9n$  Alice take the first decimal digit (from the left) and writes it onto a blackboard. She selected  $n$  so that among the nine digits on the blackboard there is the least possible number of different digits. What is this number of different digits equals to?

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