
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, the curve C1 is defined by the equation $x^2+y^2=1$. If we stretch all the points on curve C1's x-coordinates by a factor of $\sqrt{2}$ and the y-coordinates by a factor of $\sqrt{3}$, we obtain curve C2.
(1) Write out the parametric equations for curve C2.
(2) Find the point P on curve C2 such that the distance from P to the line $l: x+y-4\sqrt{5}=0$ is maximized. Also, find the maximum distance.

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