
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 right triangle $XYZ$, medians are drawn from points $X$ and $Y$ to segments $\overline{YZ}$ and $\overline{XZ}$, respectively, dividing these segments in half. The lengths of the medians from $X$ and $Y$ are 5 units and $3\sqrt{5}$ units, respectively. The area of triangle $XYZ$ is 30 square units. Determine the length of segment $\overline{XY}$.

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