
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
If
\begin{align*}
x + y + z &= 2, \\
x^2 + y^2 + z^2 &= 6, \\
x^3 + y^3 + z^3 &= 8,
\end{align*}
find $x^4 + y^4 + z^4.$

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