
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 all possible values of the expression:
\[
\frac{k a^2 b^2 + a^2 c^2 + b^2 c^2}{(a^2 - bc)(b^2 - ac) + (a^2 - bc)(c^2 - ab) + (b^2 - ac)(c^2 - ab)}.
\]
where \( k \) is a nonzero constant.

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