
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
Suppose on a parabola with vertex \( V \) and focus \( F \), there exists a point \( B \) such that \( BF = 24 \) and \( BV = 25 \). What is twice the sum of all possible values of the length \( FV \)?
A) 6
B) 7
C) 8
D) 9

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