
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:
- \( O \) is the origin of the coordinate system,
- \( N(1,0) \),
- \( M \) is a moving point on the line \( x=-1 \),
- The bisector of \( \angle MON \) intersects line \( MN \) at point \( P \),
- The locus of point \( P \) is denoted as curve \( E \).

(1) Find the equation of curve \( E \);

(2) A line \( l \) passing through point \( Q\left(-\frac{1}{2},-\frac{1}{2}\right) \) with slope \( k \) intersects 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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