
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 ancient Chinese mathematical masterpiece "Nine Chapters on the Mathematical Art," there is a method called "Kaili Circle Method," which states: "Place the product of the lengths of the sides, multiply it by sixteen, divide by nine and add one. The cube root of the result is the diameter of the circle." The "Kaili Circle Method" is equivalent to providing an approximate formula for the diameter $d$ of a known sphere with volume $V$ as $d≈\sqrt[3]{\frac{16V}{9}}$. If the surface area of the sphere is $\frac{4π}{9}$, the volume of the sphere obtained using the "Kaili Circle Method" is approximately ______.

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