
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 $\begin{cases} x=2\cos \alpha \\ y= \frac { \sqrt {3}}{3}\sin \alpha\end{cases}$ ($\alpha$ is the parameter). By reducing the x-coordinates of all points on curve $C_{1}$ to half of their original values and extending the y-coordinates to $\sqrt {3}$ times their original values, we obtain curve $C_{2}$. In the polar coordinate system (with the same unit length as the Cartesian coordinate system $xOy$, and with the origin $O$ as the pole and the non-negative half-axis of $x$ as the polar axis), the polar equation of line $l$ is $\rho\cos (\theta+ \frac {\pi}{4})=-2 \sqrt {2}$.  
$(1)$ Find the Cartesian equations of line $l$ and curve $C_{2}$;  
$(2)$ Let point $Q$ be a moving point on curve $C_{2}$, find the maximum distance from it to line $l$.

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