
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
Find the function \( w = f(z) \) that conformally maps the unit circle onto itself and satisfies the conditions

\[ 
f\left(\frac{i-1}{2}\right) = 0, \quad \arg f^{\prime}\left(\frac{i-1}{2}\right) = \frac{\pi}{2} 
\]

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