
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
Solve the equation $|x|^3 - |x|^2 - 6|x| + 8 = 0$ and find the sum and product of the roots.
A) Sum is $0$, Product is $16$
B) Sum is $8$, Product is $32$
C) Sum is $0$, Product is $32$
D) Sum is $8$, Product is $16$

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