
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 \( a + b + c = 0 \). Find all possible values of:
\[
\frac{a^4 b^4 + a^4 c^4 + b^4 c^4}{(a^2 - bc)^2 (b^2 - ac)^2 (c^2 - ab)^2}.
\]

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