
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, with the origin O as the pole and the non-negative half-axis of the x-axis as the polar axis, a polar coordinate system is established. The polar equation of curve C is $\rho=4\cos\theta$ ($0 \leq \theta \leq \frac{\pi}{2}$), and the parametric equation of line l is $\begin{cases} x=-3+t\cos \frac{\pi}{6} \\ y=t\sin \frac{\pi}{6}\end{cases}$ (t is the parameter).
(1) Find the Cartesian equation of line l and the parametric equation of curve C;
(2) Find the range of distances from a moving point M on curve C to line l.

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