
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 curve $C_{1}$ with the parametric equations $\begin{cases} x=2\cos \theta \\ y= \sqrt {3}\sin \theta\end{cases}$ (where $\theta$ is the parameter), and taking the origin $O$ as the pole and the non-negative half-axis of $x$ as the polar axis, with the same unit length, a polar coordinate system is established. The polar equation of curve $C_{2}$ is $\rho=2$.  
$(1)$ Write the ordinary equation of curve $C_{1}$ and the rectangular coordinate equation of curve $C_{2}$;  
$(2)$ Given that $M$ and $N$ are respectively the upper and lower vertices of curve $C_{1}$, and point $P$ is any point on curve $C_{2}$, find the maximum value of $|PM|+|PN|$.

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