
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 ellipse C: $$\frac{{x}^{2}}{{a}^{2}}+ \frac{{y}^{2}}{{b}^{2}}=1$$ (where $a>b>0$) passes through the point $(0, \sqrt{2})$, and satisfies $a+b=3\sqrt{2}$.
1. Find the equation of ellipse C.
2. If a line with a slope of $\frac{1}{2}$ intersects ellipse C at two distinct points A and B, and the point M has coordinates $(2,1)$, let the slopes of line MA and MB be $k_1$ and $k_2$ respectively. Is $k_1+k_2$ a constant value? Please explain your reasoning.

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