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

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