
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 the ellipse is $\left\{\begin{matrix}x= \sqrt{3}\cos \theta \\ y=\sin \theta\end{matrix}\right.$ (where $\theta$ is the parameter). With $O$ as the pole and the positive $x$-axis as the polar axis, the polar equation of the line is $2\rho\cos (\theta+ \frac{\pi}{3})=3 \sqrt{6}$. Find the maximum and minimum distances from points on the ellipse to the line.

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