
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 a right triangular cone $S-ABC$, the side edge $SA$ is perpendicular to the face $ABC$, $SA=2$; in the base triangle $ABC$, $\angle ABC=90^\circ$, $AB=2$, $BC=1$. The ratio of the volume of this right triangular cone to the volume of its circumscribed sphere is equal to ___.

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