
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 $x\_1$ and $x\_2$ ($x\_1 \neq x\_2$) be two extreme points of the function $f(x)=ax^{3}+bx^{2}-a^{2}x$ ($a > 0$).
1. If $x\_1=-1$ and $x\_2=2$, find the analytic expression of the function $f(x)$.
2. If $|x\_1|+|x\_2|=2 \sqrt {2}$, find the maximum value of $b$.

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