
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 that the sum of the distances from point M to fixed points F₁(-2, 0) and F₂(2, 0) is $4\sqrt{2}$.
(1) Find the equation of the trajectory C of point M;
(2) Let N(0, 2), draw a line l through point P(-1, -2) intersecting the ellipse C at two points A and B different from N, and the slopes of lines NA and NB are k₁ and k₂, respectively. Determine whether k₁ + k₂ is a fixed value. If it is, find the value.

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