
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 numbers $z\_1=2-i$ and $z\_2=1-3i$, find the imaginary part of the complex number $\frac{i}{z\_1} + \frac{\overline{z\_2}}{5}$ (where $\overline{z\_2}$ is the conjugate of $z\_2$).

A) $1$
B) $-1$
C) $\frac{1}{2}$
D) $-\frac{1}{2}$

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