
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, with the origin as the pole and the positive x-axis as the polar axis, a polar coordinate system is established. It is known that the parametric equation of curve C<sub>1</sub> is $$\begin{cases} x=2\cos\alpha \\ y=2+2\sin\alpha\end{cases}$$ (where $\alpha$ is the parameter), and the equation of curve C<sub>2</sub> is $x^2+(y-4)^2=16$.  
(I) Find the polar equation of curve C<sub>1</sub>.  
(II) If the curve $\theta= \frac{\pi}{3}$ ($\rho>0$) intersects with curves C<sub>1</sub> and C<sub>2</sub> at points A and B, find $|AB|$.

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