
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 $C$ is $\begin{cases} x=3\cos \alpha \\ y= \sqrt {3}\sin \alpha\end{cases}$ ($\alpha$ is the parameter), with the origin as the pole and the positive half-axis of $x$ as the polar axis, a polar coordinate system is established. The polar equation of line $l$ is $\rho\cos (\theta+ \dfrac {\pi}{4})= \dfrac { \sqrt {6}}{2}$.  
$(1)$ Find the Cartesian equation of line $l$ and the standard equation of curve $C$.  
$(2)$ Let point $P$ be any point on curve $C$, find the maximum distance from point $P$ to line $l$.

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