
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 $\mathrm {P}$ be the product of the roots of the polynomial $z^8 + z^6 + z^5 + z^3 + 1 = 0$ that have a positive imaginary part. If $\mathrm {P} = r(\cos{\theta^{\circ}} + i\sin{\theta^{\circ}})$, where $r > 0$ and $0 \leq \theta < 360$, find $\theta$.

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