
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
Integers \( x \) and \( y \), with \( x > y \), satisfy \( x + y = 7 \) and \( xy = 12 \).

Integers \( m \) and \( n \), with \( m > n \), satisfy \( m + n = 13 \) and \( m^{2} + n^{2} = 97 \).

If \( A = x - y \) and \( B = m - n \), determine the value of \( A - B \).

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