
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 \(c\) 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 \(x^4 + 16c^2 = (3c^2 - 8c)x^2\) 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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