
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 numbers 1 to 1024 are written one per square on a 32 x 32 board, so that the first row is 1, 2, ..., 32, the second row is 33, 34, ..., 64 and so on. Then the board is divided into four 16 x 16 sections and the positions of these sections are rotated clockwise. Subsequently, each section is further divided into four 8 x 8 sections and these are rotated clockwise. This process continues until each board is divided into 2 x 2 parts, with each part rotated clockwise. What numbers end up on the main diagonal (from the top left to bottom right)?

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