
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 $G = 0.\overline{427}$ be an infinite repeating decimal with the digits $4$, $2$, and $7$ repeating. When $G$ is expressed as a fraction in lowest terms, find the difference between the denominator and the numerator.
A) 372
B) 472
C) 572
D) 672
E) 772

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