
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
 $\textbf{Problem 2.}$  The list of all the numbers of  $5$  different numbers that are formed with the digits  $1,2,3,4$  and  $5$  is made. 
In this list the numbers are ordered from least to greatest. Find the number that occupies the  $100th$  position in the list.

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