
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
Let  $n \ge 2$  be a positive integer, and write in a digit form \[\frac{1}{n}=0.a_1a_2\dots.\] Suppose that  $n = a_1 + a_2 + \cdots$ . Determine all possible values of  $n$ .

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