
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 curve $C\_1$: $\begin{cases}x= & -4+\cos t \
y= & 3+\sin t\end{cases}$ ($t$ is the parameter), and curve $C\_2$: $\dfrac {x^{2}}{64}+ \dfrac {y^{2}}{9}=1$.
(1) Convert $C\_1$ into a general equation, $C\_2$ into a parametric equation, and explain what kind of curves they represent.
(2) If the parameter corresponding to point $P$ on $C\_1$ is $t= \dfrac {\pi}{2}$, 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}
user