<|im_start|>system
You are a helpful assistant. You first think about the reasoning process in the mind and then provide the user with the answer. You should try to truely solve the question by yourself without cheating.  <|im_end|>
<|im_start|>user
 Let the focus of the parabola y^2 = 8x be F, and its directrix be l. Let P be a point on the parabola, and let PA be perpendicular to l, with A being the foot of the perpendicular. If the slope of line AF is -sqrt(3), then find the length of |PF|. Express your answer as a single number. Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>
<|im_start|>assistant
Let me solve this step by step.
<think>
user
8
Let the focus of the parabola y^2 = 8x be F, and its directrix be l. Let P be a point on the parabola, and let PA be perpendicular to l, with A being the foot of the perpendicular. If the slope of line AF is -sqrt(3), then find the length of |PF|. Express your answer as a single number.
test