
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 $\left\{ \begin{array}{l} x=\sqrt{3}\cos \alpha , \\ y=\sin \alpha \end{array} \right.$ ($\alpha$ is the parameter). With point $O$ as the pole and the positive half-axis of $x$ as the polar axis, the polar coordinate equation of line $l$ is $\rho \cos (\theta -\frac{\pi }{4})=2\sqrt{2}$.

(Ⅰ) Convert the polar coordinate equation of line $l$ into a Cartesian coordinate equation;

(Ⅱ) Find the maximum distance from a point $Q$ on curve $C$ to line $l$ and the coordinates of point $Q$ at this time.

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