
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 \( z = \cos \alpha + \mathrm{i}(1 - \sin \alpha) \) with \( \alpha \in \left(\frac{\pi}{2}, 2 \pi\right) \), if \( w = z^2 - 2 \mathrm{i} z \), then the locus of the point corresponding to \( w \) in the complex plane is ______.

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