
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 a sequence of polyhedra $Q_{i}$ defined recursively: $Q_{0}$ is a regular tetrahedron with volume 8. To obtain $Q_{i + 1}$, replace the midpoint triangle of every face of $Q_{i}$ by an outward-pointing regular tetrahedron that has the midpoint triangle as a face and whose edge is half the length of the edges of the tetrahedron it is attached to. Find the volume of $Q_4$.

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