
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 \(200 \, \mathrm{m}^2\). By overlapping the rugs to cover a floor area of \(140 \, \mathrm{m}^2\), the area which is covered by exactly two layers of rug is \(24 \, \mathrm{m}^2\). Calculate the area of floor which is covered by three layers of rug.

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