
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 $x = \cos \frac{2 \pi}{9} + i \sin \frac{2 \pi}{9}.$ Compute the value of
\[(2x + x^2)(2x^2 + x^4)(2x^3 + x^6)(2x^4 + x^8).\]

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