
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 system of equation   $$ 8(x^3+y^3+z^3)=73 $$     $$ 2(x^2+y^2+z^2)=3(xy+yz+zx) $$     $$ xyz=1 $$   in set  $\mathbb{R}^3$ 

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