
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: $$\frac {x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}}=1$$ ($a>b>0$) passes through the point $(0, \sqrt {2})$, and satisfies $a+b=3\sqrt {2}$.
(Ⅰ) Find the equation of ellipse C;
(Ⅱ) A line with a slope of $\frac {1}{2}$ intersects ellipse C at two distinct points A and B. The coordinates of point M are (2, 1). Let the slopes of line MA and MB be $k_1$ and $k_2$ respectively.
① If the line passes through the left vertex of the ellipse C, find the values of $k_1$ and $k_2$;
② Explore whether $k_1+k_2$ is a constant value? And explain the reason.

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