
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 $XYZ$, \(\angle YXZ = 60^\circ\) and \(\angle XYZ = 30^\circ\). Let \(XZ = 1\). Let \(N\) be the midpoint of segment \(\overline{XZ}\). Point \(B\) is located on side \(\overline{YZ}\) such that \(\overline{XB}\perp\overline{ZN}\). If segment \(\overline{YZ}\) is extended through \(Z\) to point \(W\) so that \(BW = WX\), find the length of \(YW\) in simplest form.

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