
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 curve $C_{1}$: $\frac{x^{2}}{3} + \frac{y^{2}}{4} = 1$ is given. Taking the origin $O$ of the Cartesian coordinate system $xOy$ as the pole and the positive half-axis of $x$ as the polar axis, a polar coordinate system is established with the same unit length. It is known that the line $l$: $\rho(2\cos \theta - \sin \theta) = 6$.

(Ⅰ) Write the Cartesian coordinate equation of the line $l$ and the parametric equation of the curve $C_{1}$;

(Ⅱ) Find a point $P$ on the curve $C_{1}$ such that the distance from point $P$ to the line $l$ is maximized, and find this maximum value.

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