
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
Find all real solutions of the system of equations  $\begin{cases} 
(x + y) ^3 = z  (y + z) ^3 = x  ( z+ x) ^3 = y \end{cases} $ (Based on an idea by A . Aho , J. Hop croft , J. Ullman )

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