
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
Given that a fraction \(\frac{p}{q}\) has a decimal representation where the decimal part includes the sequence of digits 171. Arrange the denominators \(q\) of all such fractions \(\frac{p}{q}\) in ascending order. What is the sum of the smallest two denominators? (Note: A repeating decimal with a period of 9 is written as a repeating decimal with a period of 0, e.g., \(0.\dot{9} = 1.\dot{0}\)).

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