
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:

a) \(x+y+z=6, \frac{1}{x}+\frac{1}{y}+\frac{1}{z}=\frac{11}{6}, xy+yz+zx=11\)

b) \(x(y+z)=2, y(z+x)=2, z(x+y)=3\)

c) \(x^{2}+y^{2}+x+y=32, 12(x+y)=7xy\)

d) \(\frac{x^{2}}{y}+\frac{y^{2}}{x}= \frac{7}{2}, \frac{1}{y}+\frac{1}{x}= \frac{1}{2}\)

e) \(x+y+z =1, xy+xz+yz=-4, x^{3}+y^{3}+z^{3}=1\)

f) \(x^2 + y^2=12, x+y+xy=9\)

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