
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 nondecreasing functions \( f: \mathbb{R} \rightarrow \mathbb{R} \) such that:
1. \( f(0)=0 \) and \( f(1)=1 \);
2. \( f(a) + f(b) = f(a) f(b) + f(a + b - ab) \) for all real numbers \( a, b \) such that \( a < 1 < b \).

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