
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
In a cube with side length 2 units, the centers of the six faces are the vertices of a smaller octahedron. Determine the ratio of the volume of the smaller octahedron to that of the cube. Provide the sum of the numerator and denominator of the simplified fraction.

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