
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
Let's call the oscillation of a function the difference between its maximum and minimum value. What can the maximum oscillation of the function \( f(x) \times g(x) \) be if it is known that the interval \([-8, 4]\) is the range of the function \( f(x) \) and the interval \([-2, 6]\) is the range of the function \( g(x) \)?

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