
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
In the diagram below, \( \overline{PQ} \parallel \overline{RS} \) and \( \angle PTU = 75^\circ \). Find \( \angle TUS \).

[asy]
unitsize(1inch);
pair P,Q,R,S,T,U;
P = (0,0);
Q=(1,0);
R = (0,0.8);
S=(1,0.8);
T = (0.35,-0.3);
U = (0.8,1.1);
draw(T--U);
draw(P--Q);
draw(R--S);
dot(P);
dot(Q);
dot(R);
dot(S);
dot(T);
dot(U);
label("$T$",T,S);
label("$U$",U,N);
label("$P$",P,W);
label("$Q$",Q,E);
label("$R$",R,W);
label("$S$",S,E);
dot(intersectionpoint(P--Q,T--U));
dot(intersectionpoint(R--S,T--U));
[/asy]

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