
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, each edge is divided into three equal segments at points A, B, C, and D. The points of division closest to each vertex are joined to form a new, smaller tetrahedron inside the original one. Find the ratio m/n of the volume of this smaller tetrahedron to that of the original tetrahedron, where m and n are relatively prime positive integers.

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