
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 the function $f(x)=ax^{3}+bx^{2}+cx$ $(a\neq 0)$ defined on $\mathbb{R}$ as an odd function, and the function takes the extreme value $1$ at $x=-1$.
1. Find the values of $a$, $b$, and $c$;
2. If for any $x_{1}$, $x_{2}\in[-1,1]$, $|f(x_{1})-f(x_{2})|\leqslant s$ holds, find the minimum value of $s$.

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