
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 $C\_1$: $\begin{cases} & x=-4+\cos t, \ & y=3+\sin t \ \end{cases}$ (with $t$ as the parameter), and $C\_2$: $\begin{cases} & x=6\cos \theta, \ & y=2\sin \theta \ \end{cases}$ (with $\theta$ as the parameter).

(1) Convert the equations of $C\_1$ and $C\_2$ into general form and explain what type of curves they represent.
(2) If the point $P$ on $C\_1$ corresponds to the parameter $t=\frac{\pi }{2}$, and $Q$ is a moving point on $C\_2$, find the minimum distance from the midpoint $M$ of $PQ$ to the line $C\_3$: $\begin{cases} & x=-3\sqrt{3}+\sqrt{3}\alpha, \ & y=-3-\alpha \ \end{cases}$ (with $\alpha$ as the parameter).

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