
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 equation  $$ x+y+z=2; $$    $$ (x+y)(y+z)+(y+z)(z+x)+(z+x)(x+y)=1; $$    $$ x^2(y+z)+y^2(z+x)+z^2(x+y)=-6. $$  

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