
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
Let the parabola $C: x=2py^2 (p > 0)$ have focus $F$ and directrix $l$. Point $A$ is on $C$, and point $B$ is on $l$, satisfying $\overrightarrow{AF}=\frac{1}{2} \overrightarrow{FB}$. Find the slope of line $AB$.

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