
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
Suppose \( a, b, \) and \( c \) are complex numbers satisfying
\[
\begin{aligned}
a^{2} &= b - c, \\
b^{2} &= c - a, \\
c^{2} &= a - b.
\end{aligned}
\]

Compute all possible values of \( a + b + c \).

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