
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 equations of curve $C_{1}$ are $\left\{\begin{array}{l}x=2\cos\alpha\\ y=2+2\sin\alpha\end{array}\right.$ (where $\alpha$ is the parameter). Taking the coordinate origin as the pole and the positive x-axis as the polar axis, the polar coordinate equation of curve $C_{2}$ is ${\rho^2}=\frac{2}{{1+{{\sin}^2}\theta}}$.  
$(1)$ Find the general equation of curve $C_{1}$ and the Cartesian equation of $C_{2}$.  
$(2)$ Given that $N$ is the center of curve $C_{1}$ and point $M$ is a moving point on curve $C_{2}$, find the maximum value of $|MN|$.

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