
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 rook, standing on the surface of the checkered cube, beats the cells, located in the same row as well as on the
continuations of this series through one or even several edges. (The picture shows an example for a  $4 \times 4 \times 4$  cube,visible cells that some beat the rook, shaded gray.) What is the largest number do not beat each other rooks can be placed on the surface of the cube  $50 \times 50 \times 50$ ?

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