
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
In the Cartesian coordinate system $xoy$, the parametric equation of line $l$ is $\begin{cases} x=2- \frac {1}{2}t \\ y=1+ \frac { \sqrt {3}}{2}t \end{cases}$ ($t$ is the parameter). In the polar coordinate system with $O$ as the pole and the non-negative half-axis of $x$ as the polar axis, the polar equation of curve $C$ is $\rho^{2}(4\cos ^{2}\theta+\sin ^{2}\theta)=16$.  
$(1)$ Write the general equation of line $l$ and the parametric equation of curve $C$;  
$(2)$ Let $M(x,y)$ be any point on curve $C$, find the range of $\sqrt {3}x+ \frac {1}{2}y$.

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