
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 two fixed points \\(M(1,0)\\) and \\(N(2,0)\\), the moving point \\(P\\) satisfies \\(|PN|= \sqrt {2}|PM|\\).  
\\((1)\\) Find the equation of the trajectory \\(C\\) of the moving point \\(P\\);  
\\((2)\\) If \\(A\\) and \\(B\\) are two different points on the trajectory \\(C\\) from part \\((1)\\), and \\(O\\) is the origin of the coordinate system. Let the slopes of lines \\(OA\\), \\(OB\\), and \\(AB\\) be \\(k_{1}\\), \\(k_{2}\\), and \\(k\\) respectively. When \\(k_{1}k_{2}=3\\), find the range of values for \\(k\\).

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