
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
Let $c = \frac{\pi}{7}.$ Determine the value of
\[
\frac{\sin 4c \cdot \sin 5c \cdot \cos 6c \cdot \sin 7c \cdot \sin 8c}{\sin 2c \cdot \sin 3c \cdot \sin 5c \cdot \sin 6c \cdot \sin 7c}.
\]
A) $-\sin \frac{\pi}{7}$   
B) $\cos \frac{\pi}{7}$   
C) $-\cos \frac{\pi}{7}$   
D) $\sin \frac{\pi}{7}$   
E) $0$

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