
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 function \( f(x) = x^3 + a x^2 + b x + c \) (where \( x \in \mathbb{R} \)), and \( a, b, c \) be distinct non-zero integers. Given that \( f(a) = a^3 \) and \( f(b) = b^3 \), find \( a + b + c \).

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