
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
Selected Exercise $4-4$: Coordinate Systems and Parametric Equations

In the rectangular coordinate system $xOy$, the parametric equations of the curve $C$ are given by $\begin{cases} & x=\cos \theta \\ & y=\sin \theta \end{cases}$, where $\theta$ is the parameter. In the polar coordinate system with the same unit length as the rectangular coordinate system $xOy$, taking the origin $O$ as the pole and the non-negative half of the $x$-axis as the polar axis, the equation of the line $l$ is given by $\sqrt{2}p \sin (\theta - \frac{\pi}{4}) = 3$.

(I) Find the Cartesian equation of the curve $C$ and the equation of the line $l$ in rectangular coordinates.

(II) Let $P$ be any point on the curve $C$. Find the maximum distance from the point $P$ to the line $l$.

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