
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
Considering $b$ is a real number selected randomly from the interval $[-20, 20]$, let $m$ and $n$ be two relatively prime positive integers such that $m/n$ is the probability that the equation $x^4 + 36b^2 = (5b^2 - 15b)x^2$ has at least two distinct real solutions. Determine $m + n$.

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