
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 parabola \( C: y^{2}=2px(p>0) \) and points \( A(a, 0) \) and \( A'(-a, 0) \) (where \( a > 0 \)). A line passing through point \( A' \) intersects the parabola at points \( P \) and \( Q \). Find the sum of the slopes of lines \( AP \) and \( AQ \).

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