
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:
\[
\begin{cases}
x^4 + y^2 + 4 = 5 y z \\
y^4 + z^2 + 4 = 5 z x \\
z^4 + x^2 + 4 = 5 x y
\end{cases}
\]

(61st Czech and Slovak Mathematical Olympiad)

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