
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 of side length 12 feet contains one large shaded square and twelve smaller, congruent shaded squares. The ratios between the side lengths of the carpet, the large shaded square, and the small shaded squares are maintained as 4:2:1 respectively. Calculate the total shaded area.

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