
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 a random number in the interval $(0, 1)$. Determine the probability that $\left\lfloor \log_2(5x) \right\rfloor - \left\lfloor \log_2 x \right\rfloor = 0$.
A) $0.505$
B) $0.605$
C) $0.705$
D) $0.805$

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