
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 $\triangle XYZ$, $\measuredangle XYZ = 30^\circ$ and $\measuredangle XZY = 90^\circ$. $XY=2$. Let $N$ be the midpoint of segment $\overline{XY}$. Find point $B$ on segment $\overline{ZY}$ such that $\overline{XB} \perp \overline{NZ}$. Calculate the length of $XB$.

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