
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 ellipse $C:\dfrac{x^2}{2}+y^2=1$ with its right focus at $F$ and the right directrix as $l$, and a point $A$ on $l$. The segment $AF$ intersects $C$ at point $B$. If $\overrightarrow{FA}=3\overrightarrow{FB}$, calculate $|\overrightarrow{AF}|$.

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