
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 $C$: $y^{2}=8x$ with focus $F$, the directrix intersects the $x$-axis at point $K$, and point $A$ is on the parabola with $|AK|= \sqrt {2}|AF|$, where $o$ is the origin. Then, $|OA|=$ ______.

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