
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
Let the origin \\(O\\) of the Cartesian coordinate system be the pole, and the positive half-axis of \\(x\\) be the polar axis, with both coordinate systems having equal units of length. The parametric equation of line \\(l\\) is given by \\( \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\\) is \\(\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\\). As \\(\alpha\\) varies, find the minimum value of \\(|AB|\\).

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