
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
Consider the polynomial \( Q(x) = x^3 + dx^2 + ex + f \) whose roots are \( \cos \frac{\pi}{5}, \cos \frac{3\pi}{5}, \) and \( \cos \frac{4\pi}{5} \). Calculate the product \( def \).
A) 0
B) -1
C) 1/16
D) 1/25

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