
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
Calculate the sum of the smallest five arguments of the complex zeros, in the form $z_k=r_k[\cos(2\pi\alpha_k) + i\sin(2\pi\alpha_k)]$, $k=1,2,\ldots, 38$, for the polynomial 
$$Q(x) = (1+x+x^2+\ldots+x^{20})^2 - x^{18}.$$
Assume $0 < \alpha_1 \le \alpha_2 \le \ldots \le \alpha_{38} < 1$ and $r_k > 0$.

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