
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 \( O \) is the origin, \( N(1,0) \), \( M \) is a moving point on the line \( x=-1 \), and the angle bisector of \(\angle M O N \) intersects the line segment \( MN \) at point \( P \):
(1) Find the equation of the locus of point \( P \);
(2) Draw a line \( l \) passing through point \( Q \left(-\frac{1}{2}, -\frac{1}{2}\right) \) with slope \( k \). If line \( l \) intersects the curve \( E \) at exactly one point, determine the range of values for \( k \).

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