
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 \( z_1, z_2, z_3, z_4, z_5 \) be the five complex roots of the equation
\[ z^5 - 3z^4 + 6z^3 - 10z^2 + 15z - 21 = 0. \]
Calculate \(\cot \left( \sum_{k = 1}^5 \operatorname{arccot} z_k \right) \).

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