
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
Suppose you have a cube with a side length of 2x. A regular octahedron is formed by joining the centers of adjoining faces of this larger cube. Calculate the ratio of the volume of this octahedron to the volume of the cube.

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