
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 triangle $\triangle ABC$, if $\angle C=90^{\circ}$, $AC=b$, $BC=a$, then the radius of the circumcircle of $\triangle ABC$ can be expressed as $r= \frac{ \sqrt{a^{2}+b^{2}}}{2}$. By using analogical reasoning, if the three lateral edges of a right triangular prism are pairwise perpendicular and have lengths of $a$, $b$, $c$, then the radius of the circumscribed sphere of the prism is $R=$ \_\_\_\_\_\_.

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