
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 provided, $\overline{PQ} \parallel \overline{RS}$ and $\angle PZT = 135^\circ$. Find $\angle TYS$.

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

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