
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 curves $C_1: \begin{cases} x = -4 + \cos t, \\ y = 3 + \sin t \end{cases}$ ($t$ is the parameter), $C_2: \begin{cases} x = 8\cos \theta, \\ y = 3\sin \theta \end{cases}$ ($\theta$ is the parameter).

(1) Convert the equations of $C_1$ and $C_2$ into standard form and explain what curves they represent.

(2) 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 $C_3: \begin{cases} x = 3 + 2t, \\ y = -2 + t \end{cases}$ ($t$ is the parameter).

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