
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
$$
z_{n}=(1+\mathrm{i})\left(1+\frac{\mathrm{i}}{\sqrt{2}}\right) \cdots\left(1+\frac{\mathrm{i}}{\sqrt{n}}\right) \left(n \in \mathbf{Z}_{+}\right),
$$

what is the value of $\left|z_{2014}-z_{2015}\right|$?

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