
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
A function $f(x)$ is defined on the closed interval $[a, b]$. The difference between the maximum and minimum values of the function $f(x)$ on this interval is called the oscillation of function $f(x)$. If the function $f(x) = x^3 - ax^2 - (b + 2)x$ defined on the interval $[-2b, 3b - 1]$ is an odd function, find the value of $a + b$ and the oscillation of function $f(x)$.

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