
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
Given \( z = \frac{1+i}{\sqrt{2}} \), calculate the value of \(\left(z^{2^2}+z^{4^2}+z^{6^2}+\cdots+z^{{24}^2}\right) \cdot \left(\frac{1}{z^{1^2}}+\frac{1}{z^{3^2}}+\frac{1}{z^{5^2}}+\cdots+\frac{1}{z^{{23}^2}}\right)\).

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