
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
Given that $D$ is a regular dodecahedron and $T$ is a tetrahedron whose vertices are the centers of four non-adjacent faces of $D$. Suppose the edge length of $D$ is $s$. Find the ratio of the volume of $D$ to that of $T$ and express it in the form $\frac{p}{q}$, where $p$ and $q$ are relatively prime integers. Then, find $p+q$.

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