
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 rectangular prism (dimensions 1 unit by 2 units by 2 units) so that the face that was a square becomes a regular octagon and each of the rectangular faces becomes a different regular polygon. What is the total volume of the removed tetrahedra?
A) $\frac{16 - 34\sqrt{2}}{3}$
B) $\frac{20 - 14\sqrt{2}}{3}$
C) $\frac{36 - 26\sqrt{2}}{3}$
D) $\frac{48 - 34\sqrt{2}}{6}$
E) $\frac{60 - 42\sqrt{2}}{6}$

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