
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
Given that $\sum_{k=1}^{20}\sin 8k = \cot \frac{x}{y}$, where angles are measured in degrees and $x$ and $y$ are relatively prime positive integers that satisfy $\frac{x}{y} < 90$, find $x+y$.

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