
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 parametric equation of line $l$ as $\begin{cases} x=1+t\cos \alpha \\ y=t\sin \alpha \end{cases}$ (where $t$ is the parameter, $0 < \alpha < \pi$), and the polar equation of curve $C$ as $\rho\sin^2\theta=4\cos\theta$.

(I) Find the Cartesian coordinate equation of curve $C$;

(II) Suppose line $l$ intersects curve $C$ at points $A$ and $B$, find the minimum value of $|AB|$.

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