
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 \(\left[x_{1}, x_{2}\right]\) as \(x_{2}-x_{1}\). If the domain of the function \(y=\left|\log _{2} x\right|\) is \([a, b]\) and the range is \([0,2]\), then the difference between the maximum and minimum lengths of the interval \([a, b]\) is \(\qquad\).

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