
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
Suppose the roots of the polynomial \( Q(x) = x^2 + dx + e \) are \( \cos{\frac{\pi}{9}} \) and \( \cos{\frac{2\pi}{9}} \). What is the product \( de \)?
A) -1/8
B) -1/27
C) -1/64
D) -5/64

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