
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 the parabola $C$: $y^{2}=2px (p > 0)$ with focus $F$, the distance from $F$ to the asymptotes of the hyperbola $\frac{x^{2}}{3}-y^{2}=1$ is $1$. A line passing through focus $F$ with slope $k$ intersects parabola $C$ at points $A$ and $B$. If $\overrightarrow{AF}=2\overrightarrow{FB}$, find the value of $k$.

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