
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 $f(x)$ be continuous on $\mathbf{R}$ with $f(0)=0$, and for all $x, y \in \mathbf{R}$, the following conditions hold:
$$
\begin{array}{c}
f(x+y) \geqslant f(x)+f(y), \\
f(x)=a x .
\end{array}
$$

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