
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 randomly from the interval $(0,1)$. What is the probability that $\lfloor\log_{10}5x\rfloor - \lfloor\log_{10}x\rfloor = 0$? Here $\lfloor x\rfloor$ denotes the greatest integer that is less than or equal to $x$.
A) $\frac{1}{9}$
B) $\frac{1}{10}$
C) $\frac{1}{8}$
D) $\frac{1}{7}$
E) $\frac{1}{6}$

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