
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 $w_1, w_2, \dots, w_{15}$ be the fifteen complex roots of the equation
\[w^{15} - 3w^{14} + 6w^{13} - 10w^{12} + \dots + 225 = 0.\]
Calculate $\cot \left( \sum_{k = 1}^{15} \operatorname{arccot} w_k \right)$.

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