
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 set \( S \) be composed of \( n \) complex numbers (where \( 2 < n < 6 \)) with modulus 1 that satisfy the following two conditions:
1. \( 1 \in S \);
2. If \( z_1 \in S \) and \( z_2 \in S \), then \( z_1 - 2z_2 \cos(\theta) \in S \), where \( \theta = \arg\left(\frac{z_1}{z_2}\right) \).
Determine the set \( S \).

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