
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 large carpet in the shape of a 12 feet by 12 feet square includes one large shaded square in the center and eight smaller, congruent shaded squares around the edges. Given the ratios $12:\text{S}=4$ and $\text{S}:\text{T}=3$, where $\text{S}$ and $\text{T}$ are the side lengths of the large central and smaller shaded squares respectively, calculate the total shaded area.

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