
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 \[z=\frac{\sqrt{3}+i}{2}.\] What is \[\left(z^{1^2}+z^{2^2}+z^{3^2}+\dots+z^{{10}^2}\right) \cdot \left(\frac{1}{z^{1^2}}+\frac{1}{z^{2^2}}+\frac{1}{z^{3^2}}+\dots+\frac{1}{z^{{10}^2}}\right)?\]
A) 20
B) 30
C) 25
D) 35

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