
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
The denominator of an irreducible fraction is one less than the square of the numerator. If 2 is added to both the numerator and the denominator, the value of the fraction becomes greater than $\frac{1}{3}$. If 3 is subtracted from both the numerator and the denominator, the fraction becomes less than $\frac{1}{10}$. Find this fraction, given that both the numerator and the denominator are single-digit numbers. Record your answer as a two-digit number, where the first digit is the numerator and the second digit is the denominator.

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