
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 principal, the caretaker, and the parent-teacher committee, not consulting each other, each bought a carpet for the school auditorium of size \(10 \times 10\). Deciding what to do, they chose to place all three carpets as shown in the picture: the first carpet \(6 \times 8\) in one corner, the second carpet \(6 \times 6\) in the opposite corner, and the third carpet \(5 \times 7\) in one of the remaining corners (all sizes are in meters).

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

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