
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
Let \(x\) be chosen at random from the interval \((0,1)\). What is the probability that \(\lfloor\log_{2}3x\rfloor - \lfloor\log_{2}x\rfloor = 0\)?
Here, \(\lfloor x \rfloor\) denotes the greatest integer that is less than or equal to \(x\).
A) \(\frac{1}{8}\)
B) \(\frac{1}{6}\)
C) \(\frac{1}{4}\)
D) \(\frac{1}{3}\)
E) \(\frac{1}{2}\)

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