
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
1. Given the complex number $z= \frac{ \sqrt {3}+i}{1- \sqrt {3}i^{2}}$, $\overset{-}{z}$ is the conjugate of $z$. Calculate the value of $z \cdot \overset{-}{z}$.
2. Compute $(\frac{ \sqrt {2}}{1-i})^{2016}+(\frac{1+i}{1-i})^{6}$ (where $i$ is the imaginary unit).

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