
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
Given that $x=-2$ and $x=4$ are the two extremum points of the function $f(x)=x^3+ax^2+bx$.

(1) Find the constants $a$ and $b$;  
(2) Determine whether $x=-2$ and $x=4$ are the local maximum or minimum points of the function $f(x)$, and explain the reason.

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