
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
Find all real solutions to the system of equations:

1. \( x_1^2 + x_2^2 + x_3^2 + x_4^2 = 4 \)
2. \( x_1 x_3 + x_2 x_4 + x_3 x_2 + x_4 x_1 = 0 \)
3. \( x_1 x_2 x_3 + x_1 x_2 x_4 + x_1 x_3 x_4 + x_2 x_3 x_4 = -2 \)
4. \( x_1 x_2 x_3 x_4 = -1 \)

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