
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 \( C: y^{2} = 2px \) with a focus \( F \) and a directrix intersecting the x-axis at \( Q \). A line passing through \( F \) intersects the parabola \( C \) at points \( A \) and \( B \). If \( \angle QBF = 90^\circ \), solve for \( |AF| - |BF| \).

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