
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 equation $x^{2}+bx+c=0$ where $b, c \in \mathbb{R}$ has real roots in the interval $\left[-1,1\right]$, and satisfies $0\leqslant 3b+c\leqslant 3$, then the range of values for $b$ is ____.

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