
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
Elective 4-4: Parametric Equations and Polar Coordinate System

In the Cartesian coordinate system $xOy$, the curve $C_{1}$ is given by the parametric equations $\begin{cases}x=2+4\cos \alpha \\ y=2 \sqrt{3}+4\sin \alpha\end{cases}$ (where $\alpha$ is the parameter). A polar coordinate system is established with the origin $O$ as the pole and the positive half-axis of $x$ as the polar axis.

(1) Find the polar equation of the curve $C_{1}$;

(2) Given that the line $C_{2}$ has an inclination angle of $\beta$ and passes through the point $(2, \sqrt{3})$, if the curve $C_{1}$ intersects with the line $C_{2}$ at points $M$ and $N$, find the maximum and minimum values of $|MN|$.

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