
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 the triangular pyramid $P-ABC$, $PA \perp$ the base $ABC$, $AB=1$, $AC=2$, $\angle BAC=60^{\circ}$, the volume is $\frac{\sqrt{3}}{3}$, then the volume of the circumscribed sphere of the triangular pyramid is $\_\_\_\_\_\_\_\_\_\_.$

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