
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 head custodian, and the parent committee, without coming to an agreement among themselves, each bought a carpet for the school auditorium measuring $10 \times 10$. After thinking about what to do, they decided to lay 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 dimensions are in meters).

Find the area of the part of the auditorium 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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