
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
Solve the system of equations:
\[
\left\{\begin{array}{l}
a + b + c = 0 \\
a^{2} + b^{2} + c^{2} = 1 \\
a^{3} + b^{3} + c^{3} = 4abc
\end{array}\right.
\]

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