
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 \( d = \frac{2\pi}{13} \). Calculate the value of:
\[
\frac{\sin 4d \cdot \sin 8d \cdot \sin 12d \cdot \sin 16d \cdot \sin 20d}{\sin 2d \cdot \sin 4d \cdot \sin 6d \cdot \sin 8d \cdot \sin 10d}

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