
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
Consider the polynomial \[P(z) = z^4 - 6z^3 + 11z^2 - 6z + 1\] with roots \(z_1, z_2, z_3, z_4\). Define a function \(f(z) = -2i\overline{z}\). Create the polynomial \[Q(z) = z^4 + Az^3 + Bz^2 + Cz + D\] whose roots are \(f(z_1), f(z_2), f(z_3), f(z_4)\). Calculate \(B + D\).
A) 58
B) 60
C) 62
D) 64

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