
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, custodian, and parent committee each bought a carpet for the school assembly hall, which has dimensions $10 \times 10$. Without agreeing with each other, they decided to place all three carpets as follows: 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 measurements are in meters).

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

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