
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 \( w = -\frac{1}{2} + \frac{\sqrt{3}}{2} i \) (where \( i^2 = -1 \)). Determine the number of distinct values that the algebraic expression \( w^m + w^n + w^l \) can take, given that \( m, n, l \) are pairwise distinct integers.

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