
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 $E$ with its center at the origin $O$, its foci on the coordinate axes, and passing through points $M(2, 1)$ and $N(2\sqrt{2}, 0)$.
(1) Find the equation of the ellipse $E$;
(2) If a line $l$ parallel to $OM$ intersects the ellipse $E$ at two distinct points $A$ and $B$, and the slopes of lines $MA$ and $MB$ are $k_1$ and $k_2$ respectively, determine whether $k_1+k_2$ is a constant. If it is, find this constant; if not, explain why.

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