
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 curves $({C}_{1}:{\begin{matrix}& x=4+\cos t\ &#y=-3+\sin t\end{matrix}}(t))$ and $({C}_{2}:{\begin{matrix}& x=6\cos θ\ &#y=2\sin θ\end{matrix}}(θ))$ are given. With the origin $O$ as the pole and the positive half of the $x$-axis as the polar axis, establish a polar coordinate system. The polar coordinate equation of the line $l$ is $ρ\cos θ-\sqrt{3}ρ\sin θ=8+2\sqrt{3}$.

(I) Find the ordinary equations of the curves $({C}_{1},{C}_{2})$;

(II) If the parameter of point $P$ on curve ${C}_{1}$ is $t=-\frac{π}{2}$, and $Q$ is a moving point on curve ${C}_{2}$, find the minimum value of the distance between the midpoint $M$ of segment $PQ$ and line $l$.

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