
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 rectangular coordinate system, the parametric equations of curve $C$ are given by: $\begin{cases} x=\sqrt{5}\cos \theta \\ y=3+\sqrt{5}\sin \theta \end{cases}$ (where $\theta$ is the parameter).
(I) Establish a polar coordinate system with the coordinate origin as the pole and the positive half of the $x$-axis as the polar axis, and find the polar equation of curve $C$.
(II) The parametric equations of line $l$ are given by: $\begin{cases} x=t\cos \alpha \\ y=t\sin \alpha \end{cases}$ (where $t$ is the parameter). If line $l$ intersects curve $C$ at points $A$ and $B$ with $|AB|=2\sqrt{3}$, find the slope of line $l$.

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