
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, what is the perimeter of polygon $PQRSU$? [asy]
import olympiad;
size(6cm); // ADJUST
pair p = (0, 8);
pair q = (4, 8);
pair r = (4, 4);
pair s = (9, 0);
pair u = (0, 0);
draw(p--q--r--s--u--cycle);
label("$P$", p, NW);
label("$Q$", q, NE);
label("$R$", r, E + NE);
label("$S$", s, SE);
label("$U$", u, SW);
label("$8$", p / 2, W);
label("$4$", p + (q - p) / 2, 2 * N);
label("$9$", s / 2, S);
draw(rightanglemark(p, u, s));
draw(rightanglemark(u, p, q));
draw(rightanglemark(p, q, r));
add(pathticks(p--q, s=6));
add(pathticks(q--r, s=6));
[/asy]

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