
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 equation of curve $C_{1}$ is $\begin{cases} x=2+2\cos \alpha \\ y=2\sin \alpha \end{cases}$, with parameter $\alpha \in (0,\pi)$. Let $M$ be a moving point on $C_{1}$, satisfying the condition $\overrightarrow{OM}=2 \overrightarrow{OP}$, where point $P$ traces the curve $C_{2}$.  
(Ⅰ) Find the standard equation of $C_{2}$.  
(Ⅱ) In the polar coordinate system with $O$ as the pole and the non-negative half-axis of $x$ as the polar axis, the ray $\theta= \frac {\pi}{3}$ intersects $C_{1}$ and $C_{2}$ at points $A$ and $B$ respectively. Calculate $|AB|$.

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