
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
Real numbers \( x \) and \( y \) are chosen independently and uniformly at random from the interval \((0,4)\). What is the probability that \( \lfloor\log_4x\rfloor=\lfloor\log_4y\rfloor \)?
**A)** \( \frac{1}{8} \)
**B)** \( \frac{1}{4} \)
**C)** \( \frac{1}{3} \)
**D)** \( \frac{1}{2} \)
**E)** \( \frac{5}{8} \)

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