
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 polar coordinate equation of curve $C\_1$ is $${{\\rho }^{2}}{+}8\\rho \\cos \\theta -6\\rho \\sin \\theta +24=0$$, and the parametric equations of curve $C\_2$ are $$\\begin{cases} & x=8\\cos \\theta, \\\\ & y=3\\sin \\theta \\end{cases}$$ where $θ$ is the parameter.

(I) Find the rectangular coordinate equation of curve $C\_1$ and the general form equation of curve $C\_2$.

(II) If the polar coordinates of point $P$ on curve $C\_1$ are $(4\\sqrt{2},\\dfrac{3\\pi }{4})$, and $Q$ is a moving point on curve $C\_2$, find the minimum distance from the midpoint $M$ of $PQ$ to the line $$C\_3:\\begin{cases} & x=3+2t \\\\ & y=-2+t \\end{cases}$$ where $t$ is the parameter.

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