
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, caretaker, and parent committee each bought a carpet for the school assembly hall, not agreeing with each other. Each carpet is sized $10 \times 10$. 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 carpets in three layers (give the answer in square meters).

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