
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 a continuous function \( f: \mathbf{R} \rightarrow \mathbf{R} \) with \( f(0) = 0 \), solve the functional inequality: 
\[ f\left(\frac{x+y}{1+xy}\right) \geqslant f(x) + f(y). \]

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