
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
The ellipse $\frac{x^2}{5} + \frac{3y^2}{5} = 1$ intersects with the line passing through point C $(-1, 0)$ with slope $k$ at points A and B.  
(1) If the midpoint of segment AB is $\left(-\frac{1}{2}, n\right)$, find the value of $k$;  
(2) Is there a fixed point M on the x-axis such that the value of $\overrightarrow{MA} \cdot \overrightarrow{MB}$ is constant? If it exists, find the coordinates of point M; if not, explain why.

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