
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 large square carpet of side length 12 feet. It is designed with one large shaded square and twelve smaller, shaded squares of varying sizes. If the ratios $12:\text{S}$ and $\text{S}:\text{T}$ are 4 and 2 respectively, and $\text{T}:\text{U}$ is also 2, where $\text{S}$, $\text{T}$, and $\text{U}$ are the side lengths of the different shaded squares, calculate the total shaded area. We have 1 square of side $\text{S}$, 4 squares of side $\text{T}$, and 8 squares of side $\text{U}$.

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