
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 vertex \( V \) and a focus \( F \), and suppose there is a point \( B \) on the parabola such that \( FB = 24 \) and \( VB = 25 \). The directrix is vertical, and the vertex \( V \) is at the midpoint of the line segment joining \( F \) and the point \( D \) on the directrix nearest to \( F \). What is the sum of all possible values for the length \( FV \)?
A) \( \frac{48}{5} \)
B) \( \frac{92}{5} \)
C) \( \frac{96}{5} \)
D) \( \frac{100}{5} \)

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