
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
For real numbers  $x$ ,  $y$  and  $z$ , solve the system of equations:  $$ x^3+y^3=3y+3z+4 $$     $$ y^3+z^3=3z+3x+4 $$     $$ x^3+z^3=3x+3y+4 $$  

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