
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
Find all values of the parameters \( a \) and \( b \) for which the inequality

\[ \left| x^2 + a x + b \right| \leqslant \frac{1}{8} \]

holds for all \( x \in [0, 1] \).

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