
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
For any real number α, let [α] denote the largest integer not exceeding α, for example, $[ $$\sqrt {2}$$]=1$, $[-π]=-4$. Let x be a positive real number. If $[log_{2}x]$ is an even number, then x is called a lucky number. What is the probability that a number chosen from the interval (0, 1) is a lucky number?

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