
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
Take the origin \\(O\\) of the Cartesian coordinate system as the pole, the positive half-axis of \\(x\\) as the polar axis, and both coordinate systems use the same unit of length. It is known that the parametric equation of line \\(l\\) is \\(\begin{cases}x=1+t\cos α \\\\ y=t\sin α\end{cases} \\) (where \\(t\\) is the parameter, \\(0 < α < π )\\), and the polar equation of curve \\(C\\) is \\(ρ\sin^{2}θ=4\cos θ \\).

\\((\\)I\\()\\) Find the Cartesian coordinate equation of curve \\(C\\).

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

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