
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
Determine all triples of real numbers \((a, b, c)\) that satisfy the following system of equations:
\[ 
\begin{cases}
a^5 = 5b^3 - 4c \\
b^5 = 5c^3 - 4a \\
c^5 = 5a^3 - 4b
\end{cases}
\]

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