
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 cone with a volume of $\dfrac{4}{3}\pi r^3$ and a trirectangular tetrahedron $S-ABC$, $AB=BC=2$, $\angle ABC=90^{\circ}$, $SA=SC$, and the plane $SAC$ is perpendicular to the plane $ABC$. If all four vertices of the trirectangular tetrahedron are on the same spherical surface, find the volume of the sphere.

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