
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 $24 \mathrm{~m}^{2}$. Determine the area of the floor covered by three layers of rug.

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