
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 $a + b + c = 0.$ For a constant $k$, find all possible values of
\[\frac{k a^2 b^2 + k a^2 c^2 + k b^2 c^2}{(a^2 - bc)(b^2 - ac) + (a^2 - bc)(c^2- ab) + (b^2 - ac)(c^2 - ab)}.\]Enter all possible values, separated by commas.

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