
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
It is known that \(a^2 + b = b^2 + c = c^2 + a\). What values can the expression \(a\left(a^2 - b^2\right) + b\left(b^2 - c^2\right) + c\left(c^2 - a^2\right)\) take?

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