
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]


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In Elective 4-4: Coordinate System and Parametric Equations
Compress the y-coordinate of each point on the circle $x^2+y^2=4$ to half of its original value to obtain a curve denoted as $C$; rotate the line $3x-2y-8=0$ counterclockwise by 90 degrees around the origin to get a line denoted as $l$.
(I) Find the equations of line $l$ and curve $C$;
(II) Calculate the maximum distance from a point on curve $C$ to line $l$.

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