
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 \([-20, 20]\). Then, \( p \) and \( q \) are two relatively prime positive integers such that \( \frac{p}{q} \) is the probability that the equation \( x^4 + 36c^2 = (5c^2 - 15c)x^2 \) 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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