
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
Let the complex numbers \( z, -z, z^2 - z + 1, z^2 + z + 1 \) correspond to the points \( A, B, C, D \) respectively in the complex plane. Given that \( |z| = 2 \) and the quadrilateral \( ABCD \) is a rhombus, and let such \( z = a + bi \) ( \( \mathrm{i} \) is the imaginary unit, \( a, b \in \mathbb{R} \) ), then \( |a| + |b| = \quad \) (provided by Fu Lexin)

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