
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
Michael selects a real number uniformly at random from the interval \([0,1000]\). Independently, Emma selects a real number uniformly at random from the interval \([0,2000]\). What is the probability that Emma's number is greater than twice Michael's number?
A) \(\frac{1}{4}\)
B) \(\frac{1}{3}\)
C) \(\frac{1}{2}\)
D) \(\frac{2}{3}\)
E) \(\frac{3}{4}\)

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