
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
Chloe chooses a real number uniformly at random from the interval \([0, 1000]\). Independently, Laurent chooses a real number uniformly at random from the interval \([0, 2000]\), and then chooses another real number \(z\) uniformly at random from the interval \([0, 500]\). What is the probability that Laurent's total number (sum of his two numbers) is greater than Chloe's number?
A) \( \frac{3}{4} \)
B) \( \frac{4}{5} \)
C) \( \frac{5}{6} \)
D) \( \frac{7}{8} \)
E) \( 0.8\overline{6} \)

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