
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 complex numbers such that
\[
a + b + c = -1, \quad ab + ac + bc = 1, \quad abc = -1.
\]
Enter the values \(a\), \(b\), \(c\), separated by commas, in any order.

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