
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 $\begin{cases} & x=2\cos \alpha \\ & y=\sin \alpha \end{cases}$ (where $\alpha$ is the parameter), and establishing a polar coordinate system with the origin as the pole and the positive half-axis of $x$ as the polar axis, the polar equation of line $l$ is $\sqrt{2}\rho \sin \left( \theta +\frac{\pi }{4} \right)=3$

$(1)$ Find the general equation of curve $C$ and the Cartesian coordinate 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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