
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 regular tetrahedron, the midpoints of the six edges are the vertices of an octahedron. Determine the ratio of the volume of the octahedron to that of the original tetrahedron. Express the result in simplest form as $m/n$ and find $m+n$.

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