
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 rectangular coordinate system $(xOy)$, the parametric equations of the curve $C\_1$ are given by $ \begin{cases} x=-4+\cos t \\ y=3+\sin t \end{cases} (t \text{ is the parameter})$, and the polar coordinate equation of the curve $C\_2$ with the origin $O$ as the pole and the positive semi-axis of $x$ as the polar axis is given by $ρ=- \dfrac{6}{ \sqrt{1+8{\sin }^{2}θ}}$.
(1) Find the Cartesian equation of the curve $C\_1$ and the rectangular coordinate equation of the curve $C\_2$;
(2) If the point $P$ on the curve $C\_1$ corresponds to the parameter $t= \dfrac {π}{2}$, and $Q$ is a moving point on the curve $C\_2$, find the minimum distance from the midpoint $M$ of $PQ$ to the line $C\_3$: $ \begin{cases} x=-3 \sqrt {3}+ \sqrt {3}α \\ y=-3-α \end{cases} (α \text{ is the parameter})$.

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