
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 plane \(xOy\), all the points on the curve \(C_{1}\): \(x^{2}+y^{2}=1\) are protracted such that their x-coordinates are stretched to \( \sqrt {3} \) times the original and y-coordinates to twice the original. As a result, we obtain curve \(C_{2}\). In the polar coordinate system with the origin \(O\) as the pole and the positive x-axis as the polar axis, the polar equation of line \(l\) is \( \rho(2\cos \theta - \sin \theta) = 6 \).  
(i) Write down the parametric equations of curve \(C_{2}\) and the Cartesian equation of line \(l\);  
(ii) On the curve \(C_{2}\), find a point \(P\) such that the distance \(d\) from \(P\) to line \(l\) is maximum, and calculate this maximum value.

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