
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
Corners are sliced off a cube of side length 2 so that the six faces each become regular octagons, with each edge of the cube divided equally into three segments of equal length. What is the total volume of the removed tetrahedra?
A) $\frac{16}{81}$
B) $\frac{24}{81}$
C) $\frac{32}{81}$
D) $\frac{40}{81}$
E) $\frac{48}{81}$

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