
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 in the Cartesian coordinate system \(xOy\), the equation of the ellipse \(C\) is \( \frac {y^{2}}{16}+ \frac {x^{2}}{4}=1\). With \(O\) as the pole and the non-negative half-axis of the \(x\)-axis as the polar axis, set up a polar coordinate system with the same unit length. The polar equation of line \(l\) is \(\rho\sin (\theta+ \frac {\pi}{3})=3\).
\((1)\) Find the rectangular coordinate equation of line \(l\) and the parametric equation of ellipse \(C\);
\((2)\) Let \(M(x,y)\) be any point on the ellipse \(C\), find the maximum value of \(|2 \sqrt {3}x+y-1|\).

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