
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
In the Cartesian coordinate system $xOy$, with the origin $O$ as the pole and the positive half-axis of $x$ as the polar axis, a polar coordinate system is established. It is known that the curve $C_1$ is defined by $\begin{cases} & x=-4+\cos t \\ & y=3+\sin t \end{cases}$ (where $t$ is a parameter), and the curve $C_2$ is defined by $\begin{cases} & x=8\cos \theta \\ & y=3\sin \theta \end{cases}$ (where $\theta$ is a parameter).

(Ⅰ) Convert the equations of $C_1$ and $C_2$ into standard equations.

(Ⅱ) If the point $P$ on $C_1$ corresponds to the parameter $t=\frac{\pi}{2}$, and $Q$ is a moving point on $C_2$, find the minimum distance from the midpoint $M$ of $PQ$ to the line $C_3: \rho (\cos \theta -2\sin \theta )=7$.

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