
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
Two numbers, \( x \) and \( y \), are randomly selected from the interval \((0,1)\). What is the probability that \(\left\lfloor \log _{2} x \right\rfloor = \left\lfloor \log _{2} y \right\rfloor \)? If necessary, round the answer to two decimal places. Note that \([a]\) denotes the greatest integer less than or equal to \(a\).

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