
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 $a, b, c$ be complex numbers such that $|a| = 2, |b| = 2, |c| = 2$ and the equation
\[
\frac{a^3}{bc} + \frac{b^3}{ac} + \frac{c^3}{ab} = 0
\]
holds. Determine all possible values of $|a + b + c|$.

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