
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, the parametric equation for the line $l$ is given by:
$$
\begin{cases} 
x = 2 - \frac{1}{2} t \\
y = 1 + \frac{\sqrt{3}}{2} t
\end{cases} \quad (t \text{ is the parameter})
$$
Establishing a polar coordinate system with the origin $O$ as the pole and the non-negative half-axis of the $x$-axis as the polar axis, the polar equation of curve $C$ is $\rho^2(4\cos^2\theta + \sin^2\theta) = 16$.
(1) Write the standard 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 values for $\sqrt{3}x + \frac{1}{2}y$.

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