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

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

(Ⅱ) Find the maximum value of the function $f(x)$ on the interval $x\in [0,2]$.

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