
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
Given the polynomial:
\[Q(x) = (x^2 - ax + p)(x^2 - bx + q)(x^2 - 6x + 18)\]
where the polynomial has exactly four distinct complex roots and \(p + q = 12\). Determine the value of \(|b-a|\) where \(a\) and \(b\) are real numbers and \(p, q > 0\).
A) 4
B) 6
C) 8
D) 10

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