
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 \( \begin{cases} x=2\cos \alpha \\ y= \sqrt{5}\sin \alpha \end{cases} (\alpha \) is the parameter), with the origin \(O\) as the pole and the positive \(x\)-axis as the initial line, a polar coordinate system is established. The polar equation of line \(l\) is \(\rho\cos (\theta- \frac{\pi}{4})=2\sqrt{2}\).  
(1) Find the Cartesian equation of curve \(C\) and the Cartesian equation of line \(l\);  
(2) Suppose point \(P\) is a moving point on curve \(C\), find the maximum distance of point \(P\) to line \(l\) and the corresponding Cartesian coordinates of point \(P\).

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