
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 the polynomial \( P(z) = z^3 + 3z^2 + 2z + 4 \) have three complex roots \( z_1, z_2, z_3 \). Define a function \( f(z) = \overline{z} + 1 \). Let \( Q(z) = z^3 + Az^2 + Bz + C \) be the polynomial whose roots are \( f(z_1), f(z_2), f(z_3) \). Compute \( B + C \).
A) 3
B) -3
C) 4
D) -4

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