
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, if $\angle XYZ = 72^\circ$, what is the measure of $\angle XWZ$?
```
[asy]
size(6cm);
pair x = (0, 0); pair w = dir(180 - 36); pair z = dir(180 + 36); pair y = 1.3 * dir(36); pair v = 2 * 1.3 * Cos(72) * dir(-36);
draw(w--v--y--z--cycle);
label("$W$", w, N); label("$Y$", y, N); label("$X$", x, 1.5 * S); label("$Z$", z, S); label("$V$", v, SE);
add(pathticks(w--x, s=4));
add(pathticks(z--x, s=4));
add(pathticks(y--x, 2, spacing=0.9, s=4));
add(pathticks(y--v, 2, spacing=0.9, s=4));
[/asy]
```

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