
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 \[P(z) = z^4 + 6z^3 + 2z^2 + 4z + 1\] with roots denoted as $z_1, z_2, z_3, z_4$. Define a function $g(z) = 2i\overline{z}$. Let \[R(z) = z^4 + Mz^3 + Nz^2 + Lz + K\] be the polynomial whose roots are $g(z_1)$, $g(z_2)$, $g(z_3)$, and $g(z_4)$. Determine $N + K$.
A) 16
B) 8
C) -8
D) 0
E) 4

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