
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, curve $C_1: x^2+y^2=1$ is given. Taking the origin O of the Cartesian coordinate system xOy as the pole and the positive half-axis of x as the polar axis, a polar coordinate system is established with the same unit length. It is known that the line $l: \rho(2\cos\theta-\sin\theta)=6$.  
(1) After stretching all the x-coordinates and y-coordinates of points on curve $C_1$ by $\sqrt{3}$ and 2 times respectively, curve $C_2$ is obtained. Please write down the Cartesian equation of line $l$ and the parametric equation of curve $C_2$;  
(2) Find a point P on curve $C_2$ such that the distance from point P to line $l$ is maximized, and calculate this maximum value.

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