
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 the polynomial
\[ f(x)=x^{3}+a x^{2}+b x+c \quad (a, b, c \in \mathbf{R}). \]

If for any non-negative real numbers \( x \) and \( y \), it holds that
\[ f(x+y) \geqslant f(x) + f(y), \]

find the conditions that \( a \), \( b \), and \( c \) must satisfy.

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