
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 curve \\(C_{1}\\) as \\(\begin{cases}x=3\cos \alpha \\ y=\sin \alpha\end{cases} (\alpha\\) is the parameter\\()\\), and taking the origin \\(O\\) of the Cartesian coordinate system \\(xOy\\) as the pole and the positive half-axis of \\(x\\) as the polar axis to establish a polar coordinate system, the polar equation of curve \\(C_{2}\\) is \\(\rho\cos \left(\theta+ \dfrac{\pi}{4}\right)= \sqrt{2} \\).

\\((\\)Ⅰ\\()\\) Find the Cartesian equation of curve \\(C_{2}\\) and the maximum value of the distance \\(|OP|\\) from the moving point \\(P\\) on curve \\(C_{1}\\) to the origin \\(O\\);

\\((\\)Ⅱ\\()\\) If curve \\(C_{2}\\) intersects curve \\(C_{1}\\) at points \\(A\\) and \\(B\\), and intersects the \\(x\\)-axis at point \\(E\\), find the value of \\(|EA|+|EB|\\).

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