
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 curve $C_{1}: \begin{cases} x=1+2t \\ y=2-2t \end{cases} (t$ is a parameter, $t\in\mathbb{R})$, and the curve $C_{2}: \begin{cases} x=2\cos \theta +2 \\ y=2\sin \theta \end{cases} (\theta$ is a parameter, $\theta\in[0,2\pi])$.

(Ⅰ) Taking $O$ as the pole and the positive $x$-axis as the polar axis, establish a polar coordinate system with the same unit of length, and find the polar equation of the curve $C_{2}$;

(Ⅱ) If the curve $C_{1}$ intersects with the curve $C_{2}$ at points $A$ and $B$, find $|AB|$.

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