
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 \(a\), \(b\), and \(c\) be nonzero real numbers such that \(a + b + c = 0.\) Simplify
\[
\frac{1}{b^3 + c^3 - a^3} + \frac{1}{a^3 + c^3 - b^3} + \frac{1}{a^3 + b^3 - c^3}.
\]

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