
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 quadratic function \( f(x) = ax^2 + bx + c \), where \( a, b, c \in \mathbb{R} \), and the condition \( |f(x)| \leq 1 \) holds for \( |x| \leq 1 \), determine the maximum value of \( |ax + b| \) for \( |x| \leq 1 \).

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