
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 real number pairs \((a, b)\) such that the function \( f(x) = ax + b \) satisfies the condition \( f(x) f(y) + f(x+y-xy) \leq 0 \) for all real numbers \( x, y \in [0, 1] \).

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