
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 \( C: y^2 = 8x \) with focus \( F \) and directrix \( l \), a line passing through point \( F \) intersects the parabola at points \( A \) and \( B \) and intersects the directrix at point \( P \). If \( \left| AF \right| = 3\left| FB \right| \), then calculate the length of \( \left| PF \right| \).

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