
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 curve $C\_1$ with the polar coordinate equation: $ρ = 6 \sin θ - 8 \cos θ$, and the curve $C\_2$ with the parametric equations: $\begin{cases} x = 8 \cos φ \ y = 3 \sin φ \end{cases} (φ \text{ is the parameter})$,

1. Convert $C\_1$ and $C\_2$ into rectangular coordinate equations and describe the curves they represent.
2. Given the point $P(ρ, \frac{π}{2})$ on curve $C\_1$, and $Q$ is a moving point on curve $C\_2$, find the minimum distance of the midpoint $M$ of $PQ$ to the line $l$: $\begin{cases} x = 3 + 2t \ y = -2 + t \end{cases} (t \text{ is the parameter})$.

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