
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 parametric equation of curve $C$ as $\begin{cases}x=2\cos \alpha \\\\ y=\sin \alpha\end{cases}$ ($\alpha$ is the parameter), establish a polar coordinate system with the coordinate origin as the pole and the positive half of the $x$-axis as the polar axis. The polar coordinate equation of line $l$ is given by $\sqrt{2}\rho \sin (\theta +\dfrac{\pi }{4})=3$.

(1) Find the Cartesian equation of curve $C$ and the Cartesian equation of line $l$;

(2) Find the maximum distance from any point on curve $C$ to line $l$.

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