
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 that maps the region enclosed between two circles intersecting at real points \( z = a \) and \( z = b \) (\( a < b \)) at an angle \( \pi \lambda \), \( 0 < \lambda < 1 \), onto the upper half-plane \( \operatorname{Im} w > 0 \) such that the point \( z = a \) transforms to \( w = 0 \) and the point \( z = b \) transforms to \( w = \infty \).

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