
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 extended by a factor of $k$ to form a new larger tetrahedron. The centers of the four faces of this larger tetrahedron are the vertices of a smaller tetrahedron. If $k = 2$, find the ratio of the volume of the smaller tetrahedron to that of the larger tetrahedron and express the sum of the numerator and denominator of this ratio in simplest form.

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