
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 an ellipse is 
$$
\begin{cases} 
x= \sqrt {3}\cos \theta \\
y=\sin \theta
\end{cases}
(\theta \text{ is the parameter}).
$$
With $o$ as the pole and the positive $x$-axis as the polar axis, a polar coordinate system is established. The polar equation of a 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}
user