
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>: 
$$
\begin{cases}
x=-4+\cos t \\
y=3+\sin t
\end{cases}
$$
(t is the parameter), and C<sub>2</sub>: 
$$
\begin{cases}
x=6\cos \theta \\
y=2\sin \theta
\end{cases}
$$
(θ is the parameter);
(1) Find the standard equation of C<sub>1</sub> and C<sub>2</sub>, and explain what curves they represent.  
(2) If point P on C<sub>1</sub> corresponds to 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 C<sub>3</sub>: 
$$
\begin{cases}
x=-3\sqrt{3}+ \sqrt{3}t \\
y=-3-t
\end{cases}
$$
(t is the parameter).  
(3) If Q is a moving point on curve C<sub>2</sub>, find the minimum and maximum distance from Q to the line C<sub>3</sub>.  
(4) Given point P (x, y) is a moving point on curve C<sub>1</sub>, find the range of values for 2x + y.  
(5) If x + y + a ≥ 0 always holds true, and (x, y) is on curve C<sub>1</sub>, find the range of values for the real number a.

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