
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
**Calculate the expression**
\[ a^3 (b^3 - c^3) + b^3 (c^3 - a^3) + c^3 (a^3 - b^3) \]
**and express it as a factorized form involving $(a - b)(b - c)(c - a)$ multiplied by a polynomial $q(a, b, c)$. Find $q(a, b, c)$.**

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