
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 curve C is given by: 
$$
\begin{cases} 
x= \sqrt {3}\cos\theta \\
y=2\sin\theta 
\end{cases}
(\theta\text{ is the parameter})
$$
Taking the origin O of the Cartesian coordinate system xOy as the pole and the positive half-axis of the x-axis as the polar axis, a polar coordinate system is established with the same unit length. It is known that the line l is given by: $\rho(2\cos\theta-\sin\theta)=6$.

(1) Write the Cartesian coordinate equation of line l and the general equation of curve C;  
(2) Find a point P on curve C such that the distance from point P to line l is maximized, and find this maximum value.

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