
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
Given the parametric equation of curve $C_{1}$ is $\begin{cases} x=-2+2\cos \theta \\ y=2\sin \theta \end{cases}$ (with $\theta$ as the parameter), and establishing a coordinate system with the origin as the pole and the positive half-axis of $x$ as the polar axis, the polar equation of curve $C_{2}$ is $\rho=4\sin \theta$.  
(Ⅰ) Find the coordinates of the intersection points of curves $C_{1}$ and $C_{2}$.  
(Ⅱ) Points $A$ and $B$ are on curves $C_{1}$ and $C_{2}$, respectively. When $|AB|$ is maximized, find the area of $\triangle OAB$ (where $O$ is the origin).

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