
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 $xOy$, curve $C_1$ is defined by the parametric equations $\begin{cases} x = 1 + 2t \\ y = 2 - 2t \end{cases} (t \in \mathbb{R})$, and curve $C_2$ is defined by the parametric equations $\begin{cases} x = 2\cos(\theta) + 2 \\ y = 2\sin(\theta) \end{cases} (\theta \in [0, 2\pi])$.
(I) With $O$ as the pole and the positive half of the $x$-axis as the polar axis, establish a polar coordinate system using the same unit length. Find the polar equation of curve $C_2$.
(II) If curve $C_1$ intersects curve $C_2$ at points $A$ and $B$, find $|AB|$.

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