
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 upper half-plane $\operatorname{Im} z>0$ onto the unit disk $|w|<1$ such that the point $z_{0}\left(\operatorname{Im} z_{0}>0\right)$ is mapped to the center $\boldsymbol{w}=0$ of the disk.

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