
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
Given the equation of line $l$ is $y=x+4$, and the parametric equation of circle $C$ is $\begin{cases} x=2\cos \theta \\ y=2+2\sin \theta \end{cases}$ (where $\theta$ is the parameter), with the origin as the pole and the positive half-axis of $x$ as the polar axis. Establish a polar coordinate system.
- (I) Find the polar coordinates of the intersection points of line $l$ and circle $C$.
- (II) If $P$ is a moving point on circle $C$, find the maximum value of the distance $d$ from $P$ to line $l$.

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