
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 line $\left\{\begin{array}{l}x=\sqrt{3}-\frac{1}{2}t\\ y=2+\frac{\sqrt{3}}{2}t\end{array}\right.$ (where $t$ is a parameter), find the slope of this line and use it to determine the value of the real number $k$ in the equation $kx+y+1=0$, given that they are parallel.

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