
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 $O$ is the origin, $A(2,4)$, $B$ on the parabola $y^{2}=2px (p>0)$, $F$ the focus, $M$ a point on the segment $BF$, and $\overrightarrow{BM}=2\overrightarrow{MF}$, calculate the distance from point $F$ to line $OM$ when the slope of line $OM$ is at its maximum.

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