
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 given by $\{\begin{matrix} x=\sqrt{3}\cos \theta\\ y=\sin \theta\\\end{matrix} (\theta \text{ is the parameter})$. In the polar coordinate system $((\rho,\theta))$, which has the same length unit as the cartesian coordinate system $(xOy)$, and takes the origin $O$ as the pole, and the non-negative half of the $x$-axis as the polar axis, the equation of line $l$ is given by $\sqrt{2}\rho \sin\left( \theta - \frac{\pi}{4} \right)=3$.

(1) Find the ordinary equation of curve $C$ and the cartesian coordinate equation of line $l$;
(2) Let $P$ 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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