
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 \( f(x) = x^2 + ax + b \), for any \( a, b \in \mathbb{R} \), there always exists \( t \in [0, 4] \) such that \( |f(t)| \geq m \). What is the maximum value of \( m \)?

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