
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 $z= \frac{1+ \sqrt{3}i}{ \sqrt{3}+i}$ (where $i$ is the imaginary unit), find the complex conjugate of $z$.

A) $\frac{ \sqrt{3}}{2}- \frac{1}{2}i$
B) $\frac{ \sqrt{3}}{2}+ \frac{1}{2}i$
C) $\sqrt{3}-i$
D) $\sqrt{3}+i$

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