
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 with each edge of length 2 so that the six faces each become regular octagons. What is the total volume of the removed tetrahedra?
A) $\frac{48 - 32\sqrt{2}}{3}$
B) $\frac{64 - 48\sqrt{2}}{3}$
C) $\frac{96 - 64\sqrt{2}}{3}$
D) $\frac{32(3 - 2\sqrt{2})}{3}$

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