
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 a triangle, the vertices are labeled $X$, $Y$, and $Z$. The side $XZ$ has a length of $10\sqrt{3}$ and $\angle XPY = 90^\circ$ where $P$ is the midpoint of $XZ$. The angle at $Z$ is $60^\circ$. Find the length of side $XY$.

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