
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
\[
(3x + x^2)(3x^2 + x^4)(3x^3 + x^6)(3x^4 + x^8)(3x^5 + x^{10})(3x^6 + x^{12})(3x^7 + x^{14}).
\]

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