
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 a moving point P and two fixed points A (-1, 0) and B (1, 0) on a plane, the product of the slopes of the lines connecting P to A and P to B is a constant value of -2.
(1) Find the equation of the trajectory C of the moving point P.
(2) Suppose the line $l: y = x + 1$ intersects the curve C at points M and N, calculate $|MN|$.

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