
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 \( z_1, z_2, \dots, z_{10} \) be the ten complex roots of the equation
\[ z^{10} - 3z^9 + 6z^8 - 10z^7 + \dots + 36 = 0. \]
Calculate \( \cot \left( \sum_{k=1}^{10} \operatorname{arccot} z_k \right) \).

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