
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. Calculate: $\frac{(1+i)^{3}}{i} + \frac{(\sqrt{3}+i)(\sqrt{3}-i)-4i^{2016}}{(3+4i)^{2}}$
2. Given a complex number $z$ and its conjugate $\overline{z}$ that satisfy $4z+2\overline{z}=3\sqrt{3}+i$, find the complex number $z$.

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