
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
Consider a sequence of polyhedra \( Q_i \) defined recursively. \( Q_0 \) is a cube with a side length of 1. To construct \( Q_{i+1} \), place a square pyramid with a height of 1 on each square face of \( Q_i \), where each pyramid's base is a face of the cube. Each new pyramid added has half the base side length of the pyramid added in the previous iteration to the corresponding face. Calculate the total volume of \( Q_3 \).

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