
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
Given a right-angled triangle, if we form a rectangle using the two legs as adjacent sides, the length of the rectangle's diagonal is equal to the diameter of the triangle's circumcircle. This allows us to derive the formula for the radius of the circumcircle, $r=\frac{\sqrt{a^2+b^2}}{2}$ (where $a$ and $b$ are the lengths of the two legs of the right-angled triangle). By analogy, find the formula for the radius $R$ of the circumsphere of a right triangular prism with side lengths $a$, $b$, and $c$.

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