
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 in real numbers:

$$
\left\{\begin{array}{l}
x + y - 2 + 4xy = 0 \\
y + z - 2 + 4yz = 0 \\
z + x - 2 + 4zx = 0
\end{array}\right.
$$

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