
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 parametric equation of line $L$ as $\begin{cases} x= \sqrt {3}+ \frac {1}{2}t \\ y= \frac { \sqrt {3}}{2}t\end{cases}$ (where $t$ is the parameter), and the polar equation of curve $C$ as $\rho=4$.  
$(1)$ Convert the polar equation of curve $C$ into parametric equations;  
$(2)$ If line $L$ intersects curve $C$ at points $A$ and $B$, find the length of segment $AB$.

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