
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 $a$, $b$, and $c$ be complex numbers such that $|a| = |b| = |c| = 1$ and
\[
\frac{a^3}{bc} + \frac{b^3}{ac} + \frac{c^3}{ab} = -3.
\]
Find all possible values of $|a + b + c|$.

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