
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 rectangular coordinate system $(xOy)$, the parametric equations of curve $C_{1}$ are given by: $\begin{cases} x=\sqrt{3}\cos\theta \\ y=2\sin\theta \end{cases}$ ($\theta$ is the parameter). Establish a polar coordinate system with the origin $O$ as the pole, the positive half of the $x$-axis as the polar axis, and the same unit length. It is known that the line $l$: $\rho(2\cos\theta -\sin\theta)=6$.

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

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

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