
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 curve C is $$\begin{cases} x=2\cos\theta \\ y=2+2\sin\theta\end{cases}$$ (where $\theta$ is the parameter). Taking the origin as the pole and the positive half-axis of x as the polar axis, a polar coordinate system is established.
(1) Write the polar equation of curve C;
(2) Suppose the polar coordinates of point M are ($\sqrt{2}$, $\frac{\pi}{4}$), and the line l passing through point M intersects curve C at points A and B. If $|MA|=2|MB|$, find the length of chord AB.

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