
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
Reflect the vertices of a cube with a side length of one unit along one of its space diagonals as the axis. What is the combined volume of the original cube and the cube determined by the reflected points?

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