
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
Let $\triangle XOY$ be a right-angled triangle with $m\angle XOY = 90^{\circ}$. Let $M$ and $N$ be the midpoints of legs $OX$ and $OY$, respectively. A second right triangle $\triangle XYZ$ is formed by extending line segment $OY$ to point $Z$ such that $YZ = OY$ and $\angle XYZ = 90^{\circ}$. Given that $XN=23$ and $YM=25$, and $YZ = 8$, find $XY$.

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