
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
We have a cube with side length 2 units. Each corner of the cube is sliced off in such a way that the new face at each sliced corner becomes an equilateral triangle instead of a regular octagon. What is the total volume of the removed tetrahedra?
A) $\frac{32\sqrt{3} - 10}{9}$  
B) $\frac{48\sqrt{3} - 18}{9}$  
C) $\frac{48\sqrt{3} - 16}{9}$  
D) $\frac{36\sqrt{3} - 12}{9}$  
E) $\frac{54\sqrt{3} - 20}{9}$

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