
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 two curves C<sub>1</sub> and C<sub>2</sub> defined by the parametric equations C<sub>1</sub>: $\left\{ \begin{array}{l} x = -4 + \cos(t) \\ y = 3 + \sin(t) \end{array} \right.$ (t as parameter), C<sub>2</sub>: $\left\{ \begin{array}{l} x = 8\cos(\theta) \\ y = 3\sin(\theta) \end{array} \right.$ (θ as parameter).

(1) Convert the equations of C<sub>1</sub> and C<sub>2</sub> to standard form and describe the curves they represent, respectively.

(2) If point P on C<sub>1</sub> corresponds to the parameter $t = \frac{\pi}{2}$ and Q is a moving point on C<sub>2</sub>, find the minimum distance from the midpoint M of segment PQ to the line $\left\{ \begin{array}{l} x = 3 + 2t \\ y = -2 + t \end{array} \right.$ (t as parameter).

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