
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, trapezoid $WXYZ$ has $\overline{WX}\parallel \overline{ZY}$ and $\overline{WY}\perp\overline{ZY}$. Given $YZ = 15$, $\tan Z = 2$, and $\tan X = 2.5$, what is $XY$?

[asy]
pair WW, X, Y, Z;
Z = (0,0);
Y = (15,0);
WW = (15,30);
X = (27,30);
draw(WW--X--Y--Z--WW);
label("$W$", WW, N);
label("$X$", X, N);
label("$Y$", Y, S);
label("$Z$", Z, S);
[/asy]

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