
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
Three rugs have a combined area of \( 90 \, \text{m}^2 \). When they are laid down to cover completely a floor of area \( 60 \, \text{m}^2 \), the area which is covered by exactly two layers of rug is \( 12 \, \text{m}^2 \). What is the area of floor covered by exactly three layers of rug?
- A \( 2 \, \text{m}^2 \)
- B \( 6 \, \text{m}^2 \)
- C \( 9 \, \text{m}^2 \)
- D \( 10 \, \text{m}^2 \)
- E \( 12 \, \text{m}^2 \)

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