
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 $\triangle XYZ$, point W is on side YZ such that $YW=8$ and $WZ=12$. What is the ratio of the area of $\triangle XYW$ to the area of $\triangle XWZ$? Sketch:
```
size(6cm);
pair y = (0, 0); pair w = (8, 0); pair z = (20, 0);
pair x = (5, 9);
draw(x--y--z--cycle--w);
label("$X$", x, N);
label("$Y$", y, SW);
label("$W$", w, S);
label("$Z$", z, SE);
label("$8$", midpoint(y--w), S, fontsize(10));
label("$12$", midpoint(w--z), S, fontsize(10));
```

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