
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 $a, b, c$ be real numbers. Factor the expression
\[ a^4(b^3 - c^3) + b^4(c^3 - a^3) + c^4(a^3 - b^3) \]
into the form $(a-b)(b-c)(c-a)q(a,b,c)$, where $q(a,b,c)$ is some polynomial in $a, b, c$. Find $q(a,b,c)$.

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