
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 
\[
z = \frac{1 - i}{\sqrt{2}}.
\]
What is 
\[
\left(z^{1^3} + z^{2^3} + z^{3^3} + \dots + z^{8^3}\right) \cdot \left(\frac{1}{z^{1^3}} + \frac{1}{z^{2^3}} + \frac{1}{z^{3^3}} + \dots + \frac{1}{z^{8^3}}\right)?
\]
A) 8
B) 18
C) 28
D) 36
E) 44

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