
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 $\measuredangle XZY = 45^\circ$. The segment $XY = 1$. Let $N$ be the midpoint of segment $\overline{XY}$. Point $B$ lies on segment $\overline{ZY}$ such that $\overline{XB} \parallel \overline{ZN}$. Extend segment $\overline{YZ}$ through $Z$ to point $W$ such that $BW=WB$. Find $YW$ in its simplest form.

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