
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
Given that in the Cartesian coordinate system $(xOy)$, the equation of circle $M$ is $(x-4)^{2}+y^{2}=1$. Establish a polar coordinate system with the origin $O$ as the pole, the positive semi-axis of $x$ as the polar axis, and the same unit length as the Cartesian coordinate system. The polar equation of line $l$ is $ρ\sin (θ+ \frac {π}{6})= \frac {1}{2}$.

(I) Find the Cartesian equation of line $l$ and the parametric equation of circle $M$;

(II) Find the minimum distance from a point on circle $M$ to line $l$.

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