
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 any natural number  $n > 1$  write the finite decimal expansion of  $\frac{1}{n}$  (for example we write  $\frac{1}{2}=0.4\overline{9}$  as its infinite decimal expansion not  $0.5)$ . Determine the length of non-periodic part of the (infinite) decimal expansion of  $\frac{1}{n}$ .

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