
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 scientist stores the design of their time machine in a computer, and the file is protected by a password that is a permutation of the set $\{1, 2, \ldots, 64\}$. They also design a program such that each time eight integers from 1 to 64 are inputted, the computer will indicate the order among these eight numbers in the password (from left to right). Design an operational plan that will determine this password in at most 45 inputs.

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