
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 systems of equations:
a) $\left\{\begin{array}{l}x^{2}+x y+y^{2}=7, \\ y^{2}+y z+z^{2}=13, \\ z^{2}+z x+x^{2}=19 ;\end{array}\right.$
b) $\left\{\begin{array}{l}x y+x z=x^{2}+2, \\ x y+y z=y^{2}+3, \\ x z+y z=z^{2}+4 .\end{array}\right.$

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