
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
The length of the interval $[x_1, x_2]$ is $x_2 - x_1$. Given that the function $y = 4^{|x|}$ has a domain of $[a, b]$ and a range of $[1, 4]$, find the difference between the maximum and minimum possible values of the length of the interval $[a, b]$.

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