
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 that the pole of the polar coordinate system is at the origin of the rectangular coordinate system, the polar axis coincides with the non-negative x-axis and they share the same unit length. The curve $C\_1$ is defined by the equation $ρ\cos θ - 2ρ\sin θ - 7 = 0$, and the curve $C\_2$ is defined by the parametric equations $\begin{cases} x = 8\cos θ \\ y = 3\sin θ \end{cases}$ (where $θ$ is the parameter).

(1) Write the rectangular equation for $C\_1$ and the general equation for $C\_2$.
(2) Given point $P(-4, 4)$, let $Q$ be a moving point on $C\_2$. Find the minimum distance from the midpoint $M$ of $PQ$ to curve $C\_1$.

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