
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
Taking the origin \\(O\\) of the Cartesian coordinate system as the pole and the positive half-axis of the \\(x\\)-axis as the polar axis, a polar coordinate system is established. The polar equation of curve \\(C\\) is given as \\(\rho\sin^2\theta=4\cos\theta\\).

\\((\\)I\\()\\) Find the Cartesian equation of curve \\(C\\);

\\((\\)II\\()\\) If the parametric equation of line \\(l\\) is \\(\begin{cases}x=1+ \dfrac{2}{ \sqrt{5}}t \\\\ y=1+ \dfrac{1}{ \sqrt{5}}t\end{cases}\\) (where \\(t\\) is the parameter), and point \\(P(1,1)\\) is given, line \\(l\\) intersects curve \\(C\\) at points \\(A\\) and \\(B\\). Find the value of \\(|PA|+|PB|\\).

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