
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 $C\_1$: $\begin{cases}x=-4+\cos α \
y=3+\sin α\end{cases} (α \text{ is a parameter})$ and $C\_2$: $\begin{cases}x=8\cos φ \
y=3\sin φ\end{cases} (θ \text{ is a parameter})$:

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 $α=\frac{π}{2}$, and $Q$ is a moving point on $C\_2$, find the minimum distance from the midpoint $M$ of $PQ$ to 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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