
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 custodian, and the parent committee, unable to agree with each other, each bought a carpet for the school auditorium measuring $10 \times 10$ meters. After thinking about what to do, they decided to place all three carpets as shown in the picture: the first carpet $6 \times 8$ meters in one corner, the second carpet $6 \times 6$ meters in the opposite corner, and the third carpet $5 \times 7$ meters in one of the remaining corners.

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

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