
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
Map the sector \(0 < \arg z < \frac{\pi}{4}\) onto the unit disk \(|w| < 1\) in such a way that the point \(z_1 = e^{i \pi / 8}\) is mapped to the center \(w_1 = 0\), and the point \(z_2 = 0\) is mapped to the point \(w_2 = 1\).

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