Conformal Map from Substrip $\{|z|<1, 0<\mathrm{Im}(z)<1/2\}$ of a Circle to Upper Half Plane

Question

Question

Find a conformal map from the region bounded by $|z|=1$, $\mathrm{Im}(z)=0$, $\mathrm{Im}(z)=\frac{1}{2}$ and the upper half plane.

Attempt

Usually I send one of the points on the boundary to zero and another to infinity, In this case my attempts are failing so I need a hint to get me started.