
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 $\begin{cases} x=2+t\cos \alpha \\ y= \sqrt {3}+t\sin \alpha\end{cases}$ (where $t$ is the parameter), and in the polar coordinate system with the origin $O$ as the pole and the positive $x$-axis as the polar axis, the polar equation of curve $C_{2}$ is $\rho=8\cos (\theta- \frac {\pi}{3})$.  
$(1)$ Find the Cartesian coordinate equation of curve $C_{2}$ and identify what type of curve it represents;  
$(2)$ If curve $C_{1}$ intersects curve $C_{2}$ at points $A$ and $B$, find the maximum and minimum values of $|AB|$.

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