
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
A coordinate system and parametric equations (Selective 4-4): In the plane rectangular coordinate system $xOy$, the parametric equations of the curve $C\_1$ are $\begin{cases} x=\cos \theta \ y=1+\sin \theta \end{cases} (\theta \text{ is the parameter})$, and the parametric equations of the curve $C\_2$ are $\begin{cases} x=2\cos \varphi \ y=\sin \varphi \end{cases} (\varphi \text{ is the parameter})$.

1. Convert the equations of $C\_1$ and $C\_2$ into ordinary equations and explain what curves they represent, respectively.
2. Establish a polar coordinate system with the coordinate origin as the pole and the positive semi-axis of the $x$-axis as the polar axis. Given that the polar coordinate equation of line $l$ is $\rho(\cos \theta - 2\sin \theta)=4$. If the parameter corresponding to point $P$ on $C\_1$ is $\theta = \frac{\pi }{2}$, point $Q$ is on $C\_2$, and point $M$ is the midpoint of $PQ$, find the minimum distance from point $M$ to line $l$.

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