
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
Through the focus \( F \) of the parabola \( y^2 = 8(x+2) \), a line with an inclination angle of \( 60^\circ \) is drawn. If this line intersects the parabola at points \( A \) and \( B \), and the perpendicular bisector of chord \( AB \) intersects the \( x \)-axis at point \( P \), calculate the length of segment \( PF \).

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