
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
Let $x$ be a real number selected uniformly at random between $250$ and $350$. If $\lfloor \sqrt{x-50} \rfloor = 14$, find the probability that $\lfloor \sqrt{50x} \rfloor = 256$.
A) $\frac{253}{2500}$
B) $\frac{49}{500}$
C) $\frac{2}{25}$
D) $0$
E) $\frac{1}{10}$

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