
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 $Q_{i}$ where $Q_{0}$ is a regular octahedron with a volume of 8. To obtain $Q_{i+1}$, replace each face of $Q_{i}$ by an inward-pointing regular tetrahedron, such that the base of each tetrahedron is the midpoint triangle of the face and the side length of this triangle is $\frac{1}{3}$ of the original triangle. Find the volume of $Q_{3}$.

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