
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 equations of curve $C_1$ as $$\begin{cases} x=a\cos\theta \\ y=b\sin\theta \end{cases}$$ ($a>b>0$, $\theta$ is the parameter), and establishing a polar coordinate system with the origin $O$ as the pole and the positive half-axis of $x$ as the polar axis, the polar equation of curve $C_2$ is $\rho=r$ ($r>0$).  
(1) Find the general equation of curve $C_1$ and the Cartesian coordinate equation of curve $C_2$, and discuss the number of common points between the two curves;  
(2) If $b<r<a$, find the maximum value of the area of the quadrilateral formed by the intersection points of the two curves $C_1$ and $C_2$.

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