
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 the curve $C_1$ is 
$$
\begin{cases}
x=2+2\cos \alpha \\
y=2\sin \alpha
\end{cases}
(\alpha \text{ is the parameter}).
$$
With $O$ as the pole and the positive $x$-axis as the polar axis, and using the same unit length, establish a polar coordinate system.

(Ⅰ) Write out the polar coordinate equation of $C_1$;

(Ⅱ) Suppose the curve $C_2$: $\frac {x^{2}}{4}+y^{2}=1$ undergoes a scaling transformation
$$
\begin{cases}
x′= \frac {1}{2}x \\
y′=y
\end{cases}
$$
to get the curve $C_3$, the ray $\theta= \frac {\pi}{3} (\rho > 0)$ intersects $C_1$ and $C_3$ at points $A$ and $B$ respectively, find $|AB|$.

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