
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 the parabola \( C: y^2 = 2px \) with \( p > 0 \), let \( F \) be its focus, and let \( Q \) be the intersection of its directrix with the x-axis. A line passing through \( F \) intersects the parabola \( C \) at points \( A \) and \( B \). If \(\angle QBF = 90^\circ\), determine \( |AF| - |BF| \).

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