
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 $xOy$, set the origin $O$ as the pole and the positive half of the $x$-axis as the polar axis with the same unit length to establish a polar coordinate system. Suppose curve $C$ is described by the parametric equations 
$$\begin{cases}
x = \sqrt{3}\cos\theta \\
y = \sin\theta
\end{cases}$$
($\theta$ as parameter), and the polar equation of the line $l$ is $\rho\cos(\theta - \frac{\pi}{4}) = 2\sqrt{2}$.
(1) Write the standard equation of curve $C$ and the Cartesian equation of line $l$.
(2) Find the maximum distance from points on curve $C$ to line $l$ as well as the coordinates of the point where the maximum distance is attained.

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