
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 \\(O\\), its foci on the \\(x\\)-axis, and its eccentricity as \\(\dfrac{1}{2}\\), the distance from the right focus to the right vertex is \\(1\\).  
\\((1)\\) Find the standard equation of the ellipse \\(C\\);  
\\((2)\\) Does there exist a line \\(l\\) intersecting ellipse \\(C\\) at points \\(A\\) and \\(B\\) with the equation \\(y=kx+m(k∈R)\\), such that \\(|\overrightarrow{OA}+2\overrightarrow{OB}|=|\overrightarrow{OA}-2\overrightarrow{OB}|\) holds? If it exists, find the range of the real number \\(m\\); if not, explain why.

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