
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
A square carpet has a side length of 12 feet. It is designed with one large shaded square and eight smaller, congruent shaded squares. If the ratios $12:\text{S}$ and $\text{S}:\text{T}$ are $4$ and $2$ respectively, where $\text{S}$ and $\text{T}$ are the side lengths of the shaded squares, what is the total shaded area?

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