
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
Let \( b \) be a real number randomly selected from the interval \( [1, 25] \). Then, \( m \) and \( n \) are two relatively prime positive integers such that \( \frac{m}{n} \) is the probability that the equation \( x^4 + 36b^2 = (9b^2 - 15b)x^2 \) has \textit{at least} two distinct real solutions. Find the value of \( m+n \).

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