
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
(Selective 4-4: Coordinate Systems and Parametric Equations)

Given that the parametric equations of curve $C$ are $\begin{cases} x=\sqrt{3}\cos \theta \ y=\sin \theta \end{cases}$ ($\theta$ is the parameter), and the polar equation of line $l$ is $\rho\sin(\theta+\frac{\pi}{4})=2\sqrt{2}$.

(1) Write the general equation of curve $C$ and the Cartesian equation of line $l$;
(2) Let point $P$ be a moving 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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