<|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
 Given the parabola $y^{2}=4x$ with a focus at point $F$, let point $A$ be a point on the parabola in the first quadrant. A circle with a radius of $1$ and center at point $F$ intersects with line segment $AF$ at point $B$. The projection of point $A$ onto the $y$-axis is point $N$, and $|ON|=2 \sqrt {3}$. Determine the length of line segment $NB$. 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
3
Given the parabola $y^{2}=4x$ with a focus at point $F$, let point $A$ be a point on the parabola in the first quadrant. A circle with a radius of $1$ and center at point $F$ intersects with line segment $AF$ at point $B$. The projection of point $A$ onto the $y$-axis is point $N$, and $|ON|=2 \sqrt {3}$. Determine the length of line segment $NB$.
test