
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 \(a \in \mathbf{R}\) such that for any real number \(b\), the following holds:
\[
\max _{x \in[0,1]}\left|x^{2}+a x+b\right| \geqslant 1
\]
Find the range of values \(a\) can take.

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