
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
Generalizing the problem in task 55, the members of the math club found that it is possible to add not only the number 2 to the numerator of an irreducible fraction while multiplying the denominator by the same number. They found a general form of such a number. Find this number as well.

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