
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 equations of curve $C$ are given by $$\begin{cases} x=2\cos\theta \\ y=\sqrt{3}\sin\theta \end{cases}$$ (where $\theta$ is the parameter). With the origin $O$ as the pole and the positive $x$-axis as the polar axis, establish a polar coordinate system. Point $P$ has polar coordinates $(1, \frac{3\pi}{2})$, and line $l$, with slope $1$, passes through point $P$.

(I) Determine the Cartesian equation of curve $C$ and the parametric equations of line $l$;

(II) If line $l$ intersects curve $C$ at points $A$ and $B$, find the length of line segment $AB$.

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