
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 $xOy$, with the origin $O$ as the pole and the non-negative half-axis of $x$ as the polar axis, and using the same unit of length as the Cartesian coordinate system $xOy$, a polar coordinate system is established. Let the curve $C$ be given by the parametric equations $\begin{cases} x= \sqrt {3}\cos \theta \\ y=\sin \theta \end{cases}$ (with $\theta$ as the parameter), and the polar equation of line $l$ is $\rho \cos (\theta - \frac {\pi }{4})=2 \sqrt {2}$.  
$(1)$ Write the standard equation of curve $C$ and the Cartesian equation of line $l$;  
$(2)$ Find the maximum distance from a point on curve $C$ to line $l$.

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