
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
Elective 4-4; Coordinate System and Parametric Equations  
Given that the parametric equation of curve \\(C_1\\) is \\( \begin{cases} x=2\cos \phi \\ y=3\sin \phi \end{cases} \\) (with \\(\phi\\) as the parameter), and a coordinate system is established with the origin as the pole and the positive half-axis of \\(x\\) as the polar axis. The polar equation of curve \\(C_2\\) is \\(\rho=2\\). The vertices of square \\(ABCD\\) are all on \\(C_2\\), and \\(A\\), \\(B\\), \\(C\\), \\(D\\) are arranged in a counterclockwise order, with the polar coordinates of point \\(A\\) being \\((2, \frac{\pi}{3})\\).  
\\((1)\\) Find the Cartesian coordinates of points \\(A\\), \\(B\\), \\(C\\), and \\(D\\);  
\\((2)\\) Let \\(P\\) be any point on \\(C_1\\), find the range of values for \\(|PA|^2+|PB|^2+|PC|^2+|PD|^2\\).

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