
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 right directrix as $l$, point $A$ lies on $l$, and the line segment $AF$ intersects $C$ at point $B$. If $\overrightarrow{FA} = 3 \overrightarrow{FB}$, calculate the magnitude of $\overrightarrow{|AF|}$.

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