
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 $C_1$ as $\begin{cases} x=a\cos \theta \\ y=b\sin \theta \end{cases} (a > b > 0, \theta$ is the parameter), with the origin $O$ as the pole and the positive half-axis of $x$ as the polar axis, a polar coordinate system is established. 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 curves $C_1$ and $C_2$.

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