
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 $C_1$ are $$\begin{cases} x=2\cos\theta \\ y= \sqrt {3}\sin\theta\end{cases}$$ (where $\theta$ is the parameter), with the origin $O$ as the pole and the non-negative half-axis of the $x$-axis as the polar axis, establishing a polar coordinate system with the same unit length, 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 $C_2$ respectively;  
(2) Given that $M$ and $N$ are the upper and lower vertices of curve $C_1$ respectively, 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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