
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 $UVWXY$? [asy]

import olympiad;

size(6cm); // ADJUST

pair u = (0, 7);
pair v = (5, 7);

pair w = (5, 4);
pair x = (0, 0);
pair y = (9, 0);

draw(u--v--w--y--x--cycle);
label("$U$", u, NW);
label("$V$", v, NE);
label("$W$", w, E + NE);
label("$Y$", y, SE);
label("$X$", x, SW);

label("$7$", u / 2, W);
label("$5$", u + (v - u) / 2, 2 * N);
label("$9$", y / 2, S);

draw(rightanglemark(u, x, y));
draw(rightanglemark(x, u, v));
draw(rightanglemark(u, v, w));
add(pathticks(u--v, s=6));
add(pathticks(v--w, s=6));
[/asy]

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