
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
Consider all permutations of natural numbers from  $1$  to  $100$ . A permutation is called  $\emph{double}$  when it has the following property: If you write this permutation twice in a row, then delete  $100$  numbers from them you get the remaining numbers  $1, 2, 3, \ldots , 100$  in order. How many  $\emph{double}$  permutations are there?

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