
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 \([x_1, x_2]\) as $x_2 - x_1$. Given that the function $f(x) = 3^{|x|}$ has a domain of \([a, b]\) and a range of \([1, 9]\), the maximum and minimum values of the length of the interval \([a, b]\) are respectively.

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