
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
The parabola \( y = x^2 \) intersects with the line \( l \) passing through point \( P(-1, -1) \) at points \( P_1 \) and \( P_2 \).
1. Determine the range of values for the slope \( k \) of the line \( l \).
2. Find the equation of the locus of point \( Q \) on the line segment \( P_1 P_2 \) that satisfies the condition \( \frac{1}{P P_1} + \frac{1}{P P_2} = \frac{2}{P Q} \).

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