
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 director, the caretaker, and the parent committee, without agreeing with each other, each bought a carpet for the school hall with dimensions $10 \times 10$. After considering what to do, they decided to place all three carpets as shown in the picture: the first carpet of size $6 \times 8$ in one corner, the second carpet of size $6 \times 6$ in the opposite corner, and the third carpet of size $5 \times 7$ in one of the remaining corners (all sizes are in meters).

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

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