
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 line $l$ is $\left\{ \begin{array}{l} x = 3 - t, \\ y = 1 + t \end{array} \right.$ (with $t$ as the parameter). In the polar coordinate system with the origin as the pole and the positive $x$-axis as the polar axis, the curve $C$ is given by $\rho = 2\sqrt{2}\cos\left(\theta - \frac{\pi}{4}\right)$.

(I) Find the standard equation of line $l$ and the Cartesian equation of curve $C$;

(II) Find the maximum distance from points on curve $C$ to line $l$.

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