
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
A \(20 \times 20 \times 20\) cube is divided into 8000 unit cubes. A number is written in each unit cube. In each row and each column of 20 small cubes, parallel to one of the edges of the cube, the sum of the numbers is 1. In one of the small cubes, the number written is 10. Three \(1 \times 20 \times 20\) layers pass through this small cube, parallel to the faces of the cube. Find the sum of all the numbers outside of these three layers.

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