
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 $a, b, c$ be nonzero real numbers such that \( a + b + c = 0 \). Find the value of
\[
\frac{a^3 b^3}{(a^3 - b^2c)(b^3 - a^2c)} + \frac{a^3 c^3}{(a^3 - b^2c)(c^3 - a^2b)} + \frac{b^3 c^3}{(b^3 - a^2c)(c^3 - a^2b)}.
\]

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