
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 $Q(x) = x^3 + px^2 + qx + r$ are $\sin \frac{3\pi}{7}, \sin \frac{5\pi}{7},$ and $\sin \frac{\pi}{7}$. Calculate the product $pqr$.
A) $0.725$
B) $1.45$
C) $1.0$
D) $1.725$

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