
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