
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 facilities manager, and the parent committee, not agreeing with each other, each bought a rug for the school auditorium measuring $10 \times 10$ meters. Upon reflection, they decided to place all three rugs as shown in the picture: the first rug $6 \times 8$ meters in one corner, the second rug $6 \times 6$ meters in the opposite corner, and the third rug $5 \times 7$ meters in one of the remaining corners. 

Find the area of the part of the auditorium covered with rugs in three layers (give the answer in square meters).

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