
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 parametric equation of curve $C$ is $\begin{cases} x=3\sqrt{3}\cos \theta \\ y=\sqrt{3}\sin \theta \end{cases}$ ($\theta$ is the parameter), with the origin $O$ as the starting point and the positive half-axis of $x$ as the polar axis, a polar coordinate system is established. It is known that the polar coordinates of point $P$ are $(2,-\frac{\pi}{3})$, and the polar coordinate equation of line $l$ is $\rho\cos(\frac{\pi}{3}+\theta)=6$.  
(I) Find the distance from point $P$ to line $l$;  
(II) Suppose point $Q$ is on curve $C$, find the maximum distance from point $Q$ to line $l$.

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