
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 right-angled triangle $\triangle ABC$, if $\angle C=90^\circ$, $AC=b$, and $BC=a$, then the radius of the circumscribed circle of $\triangle ABC$ can be expressed as $r= \frac { \sqrt {a^{2}+b^{2}}}{2}$. By using analogy reasoning, if a tetrahedron has three side edges perpendicular to each other and their lengths are $a$, $b$, and $c$ respectively, then the radius $R$ of the circumscribed sphere of the tetrahedron is \_\_\_\_\_\_.

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