
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 $\angle PTU = 135^\circ$. Find $\angle TUS$.

[asy]
unitsize(1inch);
pair P, Q, R, S, T, U, V;
P = (0,0);
Q = (1,0);
R = (0,0.8);
S = (1,0.8);
T = (0.4, -0.3);
U = (0.6, 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);
T = intersectionpoint(P--Q, T--U);
S = intersectionpoint(R--S, T--U);
label("$P$", P, W);
label("$Q$", Q, E);
label("$R$", R, W);
label("$S$", S, E);
dot(T);
dot(S);
[/asy]

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