
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  $32 \times  32$  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  $16 \times  16$  boards and the position of these boards is moved round clockwise, so that $AB$  goes to  $DA$  $DC \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \,  CB$ then each of the  $16 \times  16 $  boards is divided into four equal  $8 \times  8$  parts and each of these is moved around in the same way (within the  $ 16 \times 16$  board). Then each of the  $8 \times  8$  boards is divided into four  $4 \times 4$  parts and these are moved around, then each  $4 \times 4$  board is divided into  $2 \times  2$  parts which are moved around, and finally the squares of each  $2 \times  2$  part are moved around. 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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