
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 $\mathrm {Q}$ be the product of the roots of $z^7 - z^5 + z^4 + z^3 + z^2 - z + 1 = 0$ that have a positive imaginary part, and suppose that $\mathrm {Q}=s(\cos{\phi^{\circ}}+i\sin{\phi^{\circ}})$, where $s>0$ and $0\leq \phi <360$. Find $\phi$.

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