
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 circles \\(C_1: x^2 + y^2 + 2x = 0\\) and \\(C_2: x^2 + y^2 - 2x - 8 = 0\\), a moving circle \\(P\\) is externally tangent to circle \\(C_1\\) and internally tangent to circle \\(C_2\\). The trajectory of the center of circle \\(P\\) is curve \\(E\\).

\\((1)\\) Find the equation of curve \\(E\\).

\\((2)\\) Suppose a line passing through the center of \\(C_2\\) intersects curve \\(E\\) at points \\(A\\) and \\(B\\). Find the range of values for \\(|AB|\\).

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