
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 the curves $C\_1$: $\begin{cases} x=-4+\cos t, \ y=3+\sin t \end{cases} (t \text{ is a parameter})$ and $C\_2$: $\begin{cases} x=8\cos \theta, \ y=3\sin \theta \end{cases} (\theta \text{ is a parameter})$.

(1) Convert the equations of $C\_1$ and $C\_2$ into ordinary equations, and explain what curves they represent.

(2) If the point $P$ on $C\_1$ corresponds to the parameter $t=\frac{π}{2}$, and $Q$ is a moving point on $C\_2$, find the minimum distance between the midpoint $M$ of $PQ$ and the line $C\_3$: $\begin{cases} x=3+2t, \ y=-2+t \end{cases} (t \text{ is a parameter})$.

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