
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 $f(x)=x^{2}+bx+c$, where $b,c \in \mathbb{R}$, if for any $x_{1}$, $x_{2} \in [-1,1]$, we have $|f(x_{1})-f(x_{2})|\leqslant 4$, determine the range of values for $b$.

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