
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 parameter equation of curve $C_1$ is $\begin{cases} x=2\cos\theta \\ y=\sqrt{3}\sin\theta \end{cases}$ ($\theta$ is the parameter), and the polar coordinate equation of curve $C_2$ is $\rho=2$ with the origin $O$ as the pole and the positive semi-axis of $x$ as the polar axis.

(I) Write the ordinary equation of $C_1$ and the rectangular coordinate equation of $C_2$;

(II) Suppose $M$ and $N$ are the upper and lower vertices of curve $C_1$, and $P$ 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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