
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
Given the expression 
\[ a^4 (b^2 - c^2) + b^4 (c^2 - a^2) + c^4 (a^2 - b^2), \]
factorize it into the form $(a - b)(b - c)(c - a) q(a, b, c)$ for some polynomial $q(a, b, c)$, and determine $q(a, b, c)$.

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