
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]


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From \( m \) boys and \( n \) girls \((10 \geqslant m > n \geqslant 4)\), 2 people are randomly chosen to be class representatives. Suppose event \( A \) denotes that the 2 chosen people are of the same gender, and event \( B \) denotes that the 2 chosen people are of different genders. If the probabilities of events \( A \) and \( B \) are the same, find the possible values of \((m, n)\).

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