
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 $U$ has a circumference of $16\pi$ inches, and segment $AB$ is a diameter. If the measure of angle $UAC$ is $30^{\circ}$, what is the length, in inches, of segment $AC$?

[asy]
size(150);
draw(Circle((0,0),17),linewidth(1));
draw((-16,-2)--(-8,-16)--(16,2)--cycle,linewidth(1));
dot((0,0));

label("U",(0,0),N);
label("A",(-16,-2),W);
label("C",(-8,-16),S);
label("B",(16,2),E);

[/asy]

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