
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
Let  $n$  be a positive integer. There is a collection of cards that meets the following properties: $\bullet$ Each card has a number written in the form  $m!$ , where  $m$  is a positive integer. $\bullet$ For every positive integer  $t\le n!$ , it is possible to choose one or more cards from the collection in such a way  $\text{   }$ that the sum of the numbers of those cards is  $t$ .
Determine, based on  $n$ , the smallest number of cards that this collection can have.

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