
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 and the positive half-axis of \\(x\\) as the polar axis, with both coordinate systems using the same unit of length. The parametric equation of line \\(l\\) is given by \\(\begin{cases} x=1+t\cos \dfrac{\pi }{4} \\ y=t\sin \dfrac{\pi }{4} \end{cases}\\) (where \\(t\\) is the parameter), 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\\), find the value of \\(|AB|\\).

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