
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) $\left\{\begin{array}{l}x+3y=4y^{3} \\ y+3z=4z^{3} \\ z+3x=4x^{3}\end{array}\right.$

b) $\left\{\begin{array}{l}2x+x^{2}y=y \\ 2y+y^{2}z=z \\ 2z+z^{2}x=x\end{array}\right.$

c) $\left\{\begin{array}{l}3\left(x+\frac{1}{x}\right)=4\left(y+\frac{1}{y}\right)=5\left(z+\frac{1}{z}\right) \\ xy+yz+xz=1\end{array}\right.$

d) $\left\{\begin{array}{c}\frac{1-x^{2}}{1+x^{2}}=\frac{2y}{1+y^{2}}=\frac{1-z^{2}}{1+z^{2}} \\ xy+yz+xz\end{array}\right.$

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