
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
A cube has a side length of $10$. Its vertices are alternately colored red and blue in such a way that each face of the cube has vertices of both colors. What is the volume of the tetrahedron whose corners are the blue vertices of the cube?

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