
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
A right triangular prism has exactly one inscribed sphere (the sphere is tangent to the two base faces and three lateral faces of the prism) and one circumscribed sphere (the sphere passes through the 6 vertices of the prism). The ratio of the surface area of the inscribed sphere to that of the circumscribed sphere is ______.

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