
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 500 and 550. If $\lfloor \sqrt{x} \rfloor = 22$, find the probability that $\lfloor \sqrt{250x} \rfloor = 350$.
A) $\frac{551}{11250}$
B) $\frac{1}{20}$
C) $\frac{1}{25}$
D) $\frac{1}{100}$
E) $\frac{1}{8}$

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