
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, the parametric equations of an ellipse are given by
$$
\begin{cases}
x= \sqrt {3}\cos\theta \\
y= \sin\theta
\end{cases} \quad (\theta \text{ is the parameter}).
$$
Using the origin O as the pole and the positive x-axis as the polar axis, we establish a polar coordinate system. The polar equation of a line is given by
$$
2\rho\cos\left(\theta+ \frac {\pi}{3}\right)=3 \sqrt {6}.
$$
Find the maximum and minimum distances from points on the ellipse to the line.

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