
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:

$$
\left\{\begin{array}{l}
x_{1} + x_{2} = x_{3}^{2} \\
x_{2} + x_{3} = x_{4}^{2} \\
x_{3} + x_{1} = x_{5}^{2} \\
x_{4} + x_{5} = x_{1}^{2} \\
x_{5} + x_{1} = x_{2}^{2}
\end{array}\right.
$$

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