Find the value of $x$ and $y$ in the following series:
$\text{U4},\text{R8},\text{O16},x,\text{I64},\text{F128},y$

Let's separate each term into its alphabetical component and its numerical component:
1. Alphabet Series: $\text{U},\text{R},\text{O},{\text{letter}}_x,\text{I},\text{F},{\text{letter}}_y$
Looking at their positional ranks in reverse order:
* $\text{U}=21$
* $\text{R}=18(21-3)$
* $\text{O}=15(18-3)$
* ${\text{letter}}_x=12(15-3)\to \text{L}$
* $\text{I}=9(12-3)$
* $\text{F}=6(9-3)$
* ${\text{letter}}_y=3(6-3)\to \text{C}$

2. Number Series: $4,8,16,{\text{num}}_x,64,128,{\text{num}}_y$
The pattern is geometric multiplication by $2$:
* $4\times 2=8$
* $8\times 2=16$
* ${\text{num}}_x=16\times 2=32$
* $64\times 2=128$
* ${\text{num}}_y=128\times 2=256$

Combining these values, $x=\text{L32}$ and $y=\text{C256}$.