
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
The school principal, the janitor, and the parent committee, unable to agree with each other, each bought a rug for the school assembly hall sized $10 \times 10$. After thinking about what to do, they decided to place all three rugs as shown in the picture: the first rug $6 \times 8$ in one corner, the second rug $6 \times 6$ in the opposite corner, and the third rug $5 \times 7$ in one of the remaining corners (all dimensions are given in meters).

Find the area of the part of the hall covered by rugs in three layers (give your answer in square meters).

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