
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
A bag contains $m$ red balls and $n$ white balls, with $m > n \geq 4$. If two balls are randomly drawn from the bag, the probability that both balls are of the same color is equal to the probability that the two balls are of different colors. Determine the number of pairs $(m, n)$ that satisfy the condition $m+n \leq 40$.

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