
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 $\angle PZT= 105^\circ$. A line segment $\overline{TU}$ intersects $\overline{RS}$ at point $U$ such that $\angle ZTU= 40^\circ$. Find $\angle ZUS$.

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

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