
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
On the ray $(0,+\infty)$ of the number line, there are several (more than two) segments of length 1. For any two different segments, you can select one number from each so that these numbers differ exactly by a factor of 2. The left end of the leftmost segment is the number $a$, and the right end of the rightmost segment is the number $b$. What is the maximum value that the quantity $b-a$ can take?

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