
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 magician and his assistant perform in front of an audience of many people.
On the stage there is an  $8$ × $8$  board, the magician blindfolds himself, and then the assistant goes inviting people from the public to write down the numbers  $1, 2, 3, 4, . . . , 64$  in the boxes they want (one number per box) until completing the  $64$  numbers. After the assistant covers two adyacent boxes, at her choice. Finally, the magician removes his blindfold and has to  $“guess”$  what number is in each square that the assistant. Explain how they put together this trick. $Clarification:$  Two squares are adjacent if they have a common side

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