
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 $[-10,10]$. Then, $p$ and $q$ are two relatively prime positive integers such that $p/q$ is the probability that the equation $x^4 + 16b^2 = (9b^2 - 15b)x^2$ has $\textit{at least}$ two distinct real solutions. Find the value of $p+q$.

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