<Tri-2025-2216>, hint

Since AD/DC=AB/BC=1/2, AD is angle bisector of <ABC. <ADB=60

Since <ADE=<30, DE//BC  AE/EB=AD/DC=1/2  thus by Ceva's theorem  

(AE/EB)(BN/NC)(CD/DA)=1 ,Line AN cuts BC in N , midpoint of BC.

Hence ABN is isosceles and AM=MN, <AMB=90

By Cosine 2nd law in APB, BMC we get PB/CM=2/3