
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 an ellipse (C): $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 (a > b > 0)$ passing through the point $(0, \sqrt{2})$, and satisfying $a + b = 3\sqrt{2}$.
(1) Find the equation of the ellipse (C);
(2) If a line with a slope of $\frac{1}{2}$ intersects the ellipse (C) at two distinct points A and B, and point M has coordinates $(2, 1)$, let the slopes of lines MA and MB be $k\_1$ and $k\_2$ respectively. Determine whether $k\_1 + k\_2$ is a constant value, and explain the reasoning.

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