
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 $C$: $y^{2}=6x$ with its focus $F$, $B$ is a point on the directrix of $C$, and $A$ is an intersection point of line $BF$ and $C$. If $\overrightarrow{FB}=3\overrightarrow{FA}$, find the distance from point $A$ to the origin.

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