
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
Define: The length of the interval $[c, d]$ (where $c < d$) is $d-c$. It is known that the function $y = | \log_2{x} |$ has a domain of $[a, b]$ and a range of $[0, 2]$. The difference between the maximum and minimum values of the length of the interval $[a, b]$ is ______.

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