
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
Let \( a \) and \( b \) be real numbers. The function \( f(x)=a x+b \) satisfies: For any \( x \in[0,1] \), \( |f(x)| \leqslant 1 \). Determine the maximum value of \( ab \).

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