
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 $f(x) = ax^3 + bx^2 + cx$ ($a \neq 0$) has extreme values at $x = \pm 1$, and $f(1) = -1$.

(1) Find the values of the constants $a$, $b$, and $c$;

(2) Determine whether $x = \pm 1$ are points of local minimum or local maximum for the function, and explain the reasons.

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