
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 the set of all fractions $\frac{x}{y}$, where $x$ and $y$ are relatively prime positive integers, determine the number of fractions that have the property that if both the numerator and denominator are increased by 2, the value of the fraction is increased by $20\%$.

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