
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 100 and 300. If $\lfloor \sqrt{x} \rfloor = 14$, find the probability that $\lfloor \sqrt{100x} \rfloor = 140$.
A) $\frac{281}{2900}$
B) $\frac{4}{29}$
C) $\frac{1}{10}$
D) $\frac{96}{625}$
E) $\frac{1}{100}$

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