
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
A parabola with vertex \(V\) and focus \(F\) has a point \(B\) such that \(BF = 26\) and \(BV = 25\). There exists a point \(M\) on segment \(BV\) such that \(M\) is the midpoint of \(BV\). Compute the sum of all possible lengths \(FV\).
A) 23
   B) 24
   C) 25
   D) 26
   E) 27

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