
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
A circle with center $X$ has a radius of 5 units, and a circle with center $Y$ has a radius of 3 units. The circles are externally tangent to each other at point $Z$. Let segment $UV$ be the common internal tangent to circles $X$ and $Y$ at points $U$ (on circle $X$) and $V$ (on circle $Y$). What is the length of segment $XY$?

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