
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 an ellipse \\(C\\) with its center at the origin and its foci on the \\(x\\)-axis, the maximum and minimum distances from a point on ellipse \\(C\\) to the foci are \\(3\\) and \\(1\\), respectively.

\\((1)\\) Find the standard equation of ellipse \\(C\\);

\\((2)\\) Let \\(P\\) be a moving point on ellipse \\(C\\), and \\({{F}\_{1}},{{F}\_{2}}\\) be the left and right foci of ellipse \\(C\\), respectively. Find the maximum and minimum values of \\(\\overrightarrow{P{{F}\_{1}}}\\cdot \\overrightarrow{P{{F}\_{2}}}\\).

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