
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 two fixed points A(-1, 0) and B(1, 0) in a plane, a line passing through a moving point M is drawn perpendicular to line AB, intersecting AB at point N. The square of the length of segment MN equals the dot product of vectors AN and BN.
1. Find the equation of the trajectory curve E of point M.
2. If line l: y = kx - 1 intersects with curve E, find the range of real number k.

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