
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 $y = \cos \frac{2 \pi}{5} + i \sin \frac{2 \pi}{5}$. Compute the value of
\[
(3y + y^2)(3y^2 + y^4)(3y^3 + y^6)(3y^4 + y^8).
\]

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