
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
There was an irreducible fraction written on the board. Petya decreased its numerator by 1 and its denominator by 2. Vasya added 1 to the numerator and left the denominator unchanged. It turned out that the boys obtained the same value. What result might they have obtained?

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