
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 $C$: $\frac{x^{2}}{2}+y^{2}=1$ with its right focus at $F$, and the line $l$: $x=2$. If point $A$ lies on line $l$, and segment $AF$ intersects ellipse $C$ at point $B$, and if $\vec{FA}=3\vec{FB}$, calculate $|\vec{AF}|$.

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