
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
Elective 4-4: Coordinate System and Parametric Equations

In the Cartesian coordinate system $xOy$, the curve $C_1$ is defined by $\begin{cases} & x=1+2t \\ & y=2-2t \\ \end{cases}$ (where $t$ is a parameter, $t \in \mathbb{R}$), and the curve $C_2$ is defined by $\begin{cases} & x=2\cos \theta +2 \\ & y=2\sin \theta \\ \end{cases}$ (where $\theta$ is a parameter, $\theta \in [0,2\pi]$).

(I) Taking $O$ as the pole and the positive half-axis of $x$ 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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