
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
Triangle $XYZ$ has sides $\overline{XY}$, $\overline{YZ}$, and $\overline{ZX}$ of length 30, 40, and 50, respectively. Let $\alpha$ be the circle circumscribed around $\triangle XYZ$. Find the radius $R$ of $\alpha$, where $R$ can be expressed as a simplified fraction.

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