
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 cube with a side length of 10 is divided into 1000 smaller cubes with an edge length of 1. A number is written in each small cube, such that the sum of the numbers in every column of 10 cubes (in any of the three directions) is equal to 0. One of the small cubes (denoted by $A$) contains the number one. Three layers, each parallel to a face of the larger cube and passing through cube $A$, have a thickness of 1. Find the sum of all numbers in the cubes that do not lie within these layers.

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