
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
Suppose curve $C\_1: \begin{cases} x=-4+\cos t \ y=3+\sin t \end{cases}$ (where $t$ is the parameter) and curve $C\_2: \frac{x^{2}}{64}+ \frac{y^{2}}{9}=1$.

(1) Convert $C\_1$ to a standard equation, $C\_2$ to a parametric equation; and explain what kind of curves they represent, respectively.

(2) If the point $P$ on $C\_1$ corresponds to the parameter $t=\frac{π}{2}$, and $Q$ is the moving point on $C\_2$, find the minimum distance from the midpoint $M$ of $PQ$ to the line $C\_3: x-2y-7=0$.

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