
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
Choose $4-4$: Parameter Equation Lecture. In the plane rectangular coordinate system $xOy$, with $O$ as the pole and the non-negative half-axis of $x$ as the polar axis, establish a polar coordinate system. The polar coordinates of point $P$ are $(2\sqrt{3}, \dfrac{\pi}{6})$. The polar coordinate equation of curve $C$ is $\rho ^{2}+2\sqrt{3}\rho \sin \theta = 1$.

(Ⅰ) Write down the rectangular coordinates of point $P$ and the general equation of curve $C.

(Ⅱ) If $Q$ is a moving point on $C$, find the minimum value of the distance from the midpoint $M$ of $PQ$ to the line $l: \left\{\begin{array}{l}x=3+2t\\y=-2+t\end{array}\right.$ (where $t$ is a parameter).

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