
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 that the roots of the polynomial $Q(x)=x^2 + dx + e$ are $\cos \frac{\pi}{5}$ and $\cos \frac{3\pi}{5}$. What is $de$?
A) 0
B) $\frac{1}{16}$
C) $-\frac{1}{16}$
D) $\frac{1}{4}$

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