
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 independently chosen at random from the interval \( (0,1) \). What is the probability that \(\lfloor \log_{10} x \rfloor = \lfloor \log_{10} y \rfloor\)?
A) $\frac{1}{2}$
B) $\frac{2}{3}$
C) $0.8182$
D) $0.9$
E) $0.99$

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