
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 $A$ has a radius of $10$ units, and a smaller circle with center $B$ has a radius of $3$ units. The circles are externally tangent to each other at point $C$. A line segment $UV$ is a common external tangent to circles $A$ and $B$ at points $U$ and $V$, respectively. If the distance between the centers $A$ and $B$ (segment $AB$) is part of your calculation, find the length of segment $AV$.

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