
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
In the Cartesian coordinate system \\(xOy\\), the parametric equations of curve \\(C_1\\) are \\(\begin{cases} & x=2\cos \alpha \\ & y=2+2\sin \alpha \end{cases}(\alpha\\) as parameter\\(). Point \\(M\\) is a moving point on \\(C_1\\), and point \\(P\\) satisfies \\(OP=2OM\\). The trajectory of point \\(P\\) is curve \\(C_2\\).

\\((1)\\) Find the equation of \\(C_2\\);

\\((2)\\) In the polar coordinate system with \\(O\\) as the pole and the positive \\(x\\)-axis as the polar axis, the ray \\(θ= \dfrac{π}{3}\\) intersects curve \\(C_1\\) and has an intersection point \\(A\\) other than the pole, and intersects curve \\(C_2\\) and has an intersection point \\(B\\) other than the pole. Find the length of \\(\left| \left. AB \right| \right|\\).

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