
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 polynomials \( f(x) \) of degree at most 3 that satisfy the condition: for any \( x, y \geq 0 \), the inequality \( f(x+y) > f(x) + f(y) \) holds.

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