
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 the complex number $z=-\frac{1}{2}+\frac{\sqrt{3}}{2}i$, where $\overline{z}$ is its conjugate, find:
(1) the modulus of the complex number $\frac{1}{z}$;
(2) the value of $(\overline{z})^2$.

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