
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 equations:

a) \(\left\{\begin{array}{l}2 x=(y+z)^{2}, \\ 2 y=(z+x)^{2}, \\ 2 z=(x+y)^{2}\end{array}\right.\)

b) \(\left\{\begin{array}{l}x^{2}-x y-x z+z^{2}=0, \\ x^{2}-x z-y z+3 y^{2}=2, \\ y^{2}+x y+y z-z^{2}=2 .\end{array}\right.\)

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