
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} (\theta\\) as 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, and the polar equation of curve \\(C_{2}\\) is \\(\rho=2\sin \theta\\).  
(Ⅰ) Find the Cartesian coordinates of the intersection points of curve \\(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\\) (\\(O\\) is the origin).

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