
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 in the Cartesian coordinate system, the parametric equation of curve $C_1$ is $$\begin{cases} x=-1+\cos\theta \\ y=\sin\theta \end{cases}$$ (where $\theta$ is the parameter). Taking the origin as the pole and the positive half-axis of the x-axis as the polar axis, a polar coordinate system is established. The polar equation of curve $C_2$ is $\rho=2\sin\theta$.  
(Ⅰ) Find the Cartesian 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}
user