
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, with the origin as the pole and the x-axis as the positive semi-axis, a polar coordinate system is established. The polar equation of circle C is $\rho=6\cos\theta$, and the parametric equation of line $l$ is 
$$
\begin{cases} 
x=3+ \frac {1}{2}t \\ 
y=-3+ \frac { \sqrt {3}}{2}t
\end{cases}
$$ 
($t$ is the parameter).

(1) Find the Cartesian coordinate equation of circle C;  
(2) Find the ratio of the lengths of the two arcs into which line $l$ divides circle C.

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