
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 \( Q \) be the product of the roots of \( z^8 + z^6 + z^5 + z^4 + z^2 + 1 = 0 \) that have a positive imaginary part, and suppose that \( Q = s(\cos{\phi^{\circ}} + i\sin{\phi^{\circ}}) \), where \( s > 0 \) and \( 0 \leq \phi < 360 \). Find \( \phi \).

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