
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
Given the complex number $\frac{1+mi}{2-i}$, its real part and imaginary part are additive inverses of each other, where $m \in \mathbb{R}$, and $i$ is the imaginary unit. Find the conjugate of the complex number $z = 4 + mi$.

A) $4 + 3i$
B) $4 - 3i$
C) $4 + 5i$
D) $4 - 5i$

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