
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 rectangular coordinate system $(xOy)$, the parametric equations of the curve $C_{1}$ are given by $\begin{cases} x=2\cos \alpha \\ y=2+2\sin \alpha \end{cases}$ ($\alpha$ is the parameter). Point $M$ moves on curve $C_{1}$, and point $P$ satisfies $\overrightarrow{OP}=2\overrightarrow{OM}$. The trajectory of point $P$ forms the curve $C_{2}$.

(I) Find the equation of $C_{2}$;

(II) In the polar coordinate system with $O$ as the pole and the positive semi-axis of $x$ as the polar axis, the ray $\theta = \dfrac{\pi}{3}$ intersects $C_{1}$ at point $A$ and $C_{2}$ at point $B$. Find the length of the segment $|AB|$.

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