
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 $z_1, z_2, \dots, z_{24}$ be the twenty-four (complex) roots of the equation
\[ z^{24} - 2z^{23} + 4z^{22} - 8z^{21} + \dots + 1024 = 0. \]
Calculate $\cot \left( \sum_{k = 1}^{24} \operatorname{arccot} z_k \right)$.

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