
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, $WXYZ$ is a trapezoid such that $\overline{WX}\parallel \overline{ZY}$ and $\overline{WY}\perp \overline{ZY}$. If $YZ = a$, $\tan Z = \sqrt{3}$, and $\tan X = \frac{1}{2}$, then what is $XY$ and what is the perimeter of triangle $WXY$?

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