
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 $\begin{cases} x=2\cos \theta \\ y=2+2\sin \theta \end{cases}$ ($\theta$ is the parameter), with the origin as the pole and the positive half-axis of $x$ as the polar axis, a polar coordinate system is established.  
(Ⅰ) Write the polar equation of curve $C$;  
(Ⅱ) 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 $B$, find $|MA|\cdot|MB|$.

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