
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 total side length of 12 feet. It includes one large central square and eight identical smaller squares in each corner and side center, as illustrated. The ratios of the side lengths of the total square carpet, the large central shaded square, and the smaller shaded squares are 4:2:1 respectively. Calculate the total perimeter of all the shaded squares combined.

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