
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
\[
a^4 (b^3 - c^3) + b^4 (c^3 - a^3) + c^4 (a^3 - b^3),
\]
factor it into the form $(a - b)(b - c)(c - a) p(a,b,c)$ and find the polynomial $p(a,b,c)$.

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