
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
Points $A$, $B$, $R$, $S$, and $C$ lie on a circle as shown. The measures of arcs $BR$ and $RS$ are $48^\circ$ and $54^\circ$, respectively. Find the sum of the measures of angles $T$ and $U$, in degrees, where $T$ is the angle formed by the intersection of chords $AC$ and $BS$, and $U$ is formed by the extension of radius $OC$ and chord $BS$.

[asy]
import graph;

unitsize(2 cm);

pair A, B, C, S, R, T, U, O;

A = dir(150);
B = dir(30);
C = dir(210);
S = dir(-45);
R = dir(60);
O = (0,0);  // Center of the circle

draw(Circle((0,0),1));
draw(B--S--C);
draw(A--C);
draw(B--R--S);

label("$A$", A, NW);
label("$B$", B, NE);
label("$C$", C, SW);
label("$R$", R, N);
label("$S$", S, SE);
label("$T$", intersectionpoint(A--C, B--S), N);
label("$U$", intersectionpoint(O--C, B--S), S);
label("$O$", O, center);
[/asy]

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