
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 $C_{1}$ is $\begin{cases} x=1+\cos \alpha \\ y=\sin \alpha \end{cases}$, where $\alpha$ is the parameter. With the origin $O$ as the pole and the non-negative half-axis of $x$ as the polar axis, a polar coordinate system is established, and the polar equation of curve $C_{2}$ is $\rho=4\sin \theta$.
- (Ⅰ) If $A$, $B$ are the common points of curves $C_{1}$ and $C_{2}$, find the slope of line $AB$;
- (Ⅱ) If $A$, $B$ are respectively moving points on curves $C_{1}$ and $C_{2}$, when $|AB|$ takes the maximum value, find the area of $\triangle AOB$.

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