
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
You have a sequence of polyhedra $Q_i$, where $Q_0$ is a regular octahedron whose volume is 1. To obtain $Q_{i+1}$, replace the midpoint triangle of every face of $Q_i$ by an outward-pointing regular octahedron that has the midpoint triangle as a base. Calculate the volume of $Q_2$. Express your answer in the form of $\frac{m}{n}$, with $m$ and $n$ being relatively prime integers and provide $m+n$.

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