
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 $C_1$: 
\[
\begin{cases} 
x=-4+\cos t \\
y=3+\sin t 
\end{cases}
\]
where \( t \) is a parameter, and the curve $C_2$: 
\[
\frac{x^2}{64}+\frac{y^2}{9}=1.
\]
(1) Convert $C_1$ to a regular equation and $C_2$ to a parametric equation; and explain what curves they represent respectively?
(2) If 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 $C_3: x-2y-7=0$.

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