
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
$$
C_{1}: \begin{cases} x=-4+\cos(t) \\ y=3+\sin(t) \end{cases} \quad (t \text{ is the parameter}),
$$
$$
C_{2}: \begin{cases} x=8\cos(\theta) \\ y=3\sin(\theta) \end{cases} \quad (\theta \text{ is the parameter}),
$$

1. Convert the equations of $C_1$ and $C_2$ into standard form and describe what those curves represent.
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
$$
C_{3}: \begin{cases} x=3+2t \\ y=-2+t \end{cases} \quad (t \text{ is the parameter}).
$$

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