
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) 
\[
\begin{cases} 
x + 3y = 4y^3 \\ 
y + 3z = 4z^3 \\ 
z + 3x = 4x^3 
\end{cases}
\]

b)
\[
\begin{cases} 
2x + x^2y = y \\ 
2y + y^2z = z \\ 
2z + z^2x = x 
\end{cases}
\]

c)
\[
\begin{cases} 
3\left(x + \frac{1}{x}\right) = 4\left(y + \frac{1}{y}\right) = 5\left(z + \frac{1}{z}\right) \\ 
xy + yz + xz = 1 
\end{cases}
\]

d)
\[
\begin{cases} 
\frac{1 - x^2}{1 + x^2} = \frac{2y}{1 + y^2} = \frac{1 - z^2}{1 + z^2} \\ 
xy + yz + xz 
\end{cases}
\]

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