
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 sequence $\left\{z_{n}\right\}$ which satisfies
$$
z_{1}=1, \quad z_{n+1}=\overline{z_{n}}+1+n \mathrm{i} \quad (n=1,2, \cdots),
$$
where $\mathrm{i}$ is the imaginary unit and $\overline{z_{n}}$ represents the complex conjugate of $z_{n}$. Determine the value of $z_{2015}$.

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