
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 $(xOy)$, the parametric equations of line $l$ are given by $ \begin{cases} x=1+t\cos \alpha \\ y=1+t\sin \alpha \end{cases} (t $ is the parameter, $\alpha$ is the inclination angle), and the polar coordinate system is established with the coordinate origin as the pole and the positive semi-axis of $x$ as the polar axis. Using the same length unit for both coordinate systems, the polar equation of curve $C$ is $\rho^{2}-4\rho\cos \theta-6\rho\sin \theta+4=0$.

(I) Find the Cartesian equation and the parametric equations of curve $C$.
(II) If line $l$ intersects curve $C$ at points $A$ and $B$, find the range of values for the line segment $|AB|$.

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