
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 \( d = \frac{\pi}{7} \). Compute the value of
\[
\frac{3 \sin 2d \cdot \sin 4d \cdot \sin 6d \cdot \sin 8d \cdot \sin 10d}{\sin d \cdot \sin 2d \cdot \sin 3d \cdot \sin 4d \cdot \sin 5d}
\]
A) 1
B) 2
C) 3
D) \( \frac{7}{2} \)
E) \( \frac{6\pi}{7} \)

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