
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
Consider a parabola with its vertex $V$ and focus $F$. There exists a point $B$ on this parabola such that $BF=24$ and $BV=25$. Determine the sum of all possible values of the length $FV$.
A) 15
B) 16
C) 17
D) 18
E) 19

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