
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
Consider the expression:
\[a(b - c)^4 + b(c - a)^4 + c(a - b)^4.\]
This expression can be factored into the form $(a - b)(b - c)(c - a)q(a,b,c)$ for some polynomial $q(a,b,c)$. Find $q(a,b,c)$.

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