
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 $\triangle XYZ$, $\measuredangle XYZ = 60^\circ$ and $\measuredangle XZY = 30^\circ$. $XZ = 2$. Let $N$ be the midpoint of segment $\overline{XZ}$. Point $B$ lies on side $\overline{ZY}$ such that $\overline{XB} \perp \overline{NY}$. Extend segment $\overline{ZY}$ through $Y$ to point $W$ such that $BW = WX$. Find $ZW$ and express it in the form $\frac{p - \sqrt{q}}{r}$ where $p$, $r$ are relatively prime positive integers, and $q$ is a positive integer. Then, determine $p+q+r$.

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