
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 \[P(z) = z^4 + 6z^3 + 7z^2 + 3z + 2\] which has roots \(z_1, z_2, z_3, z_4\). Define a function \(f(z) = 3i\overline{z}\). Let \(Q(z) = z^4 + Az^3 + Bz^2 + Cz + D\) be the polynomial whose roots are \(f(z_1), f(z_2), f(z_3), f(z_4)\). Determine \(B + D\).
A) 81
B) 99
C) 126
D) 162

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