
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
An infinite loop decimal can be converted into a rational number, such as \\(0. \\cdot 1= \\dfrac {1}{9}\\), \\(0. \\cdot 1 \\cdot 3= \\dfrac {13}{99}\\), \\(0. \\cdot 01 \\cdot 5= \\dfrac {5}{333}\\), etc. Please derive the rational number representation for \\(0.0 \\cdot 1 \\cdot 7\\) in its simplest form as \\(\\dfrac{m}{n}\\), where \\(m, n \in \mathbb{N}^*\\).

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