
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. We want to make up a collection of cards with the following properties:

1. each card has a number of the form  $m!$  written on it, where  $m$  is a positive integer.

2. for any positive integer   $ t \le n!$ , we can select some card(s) from this collection such that the sum of the number(s) on the selected card(s) is  $t$ .

Determine the smallest possible number of cards needed in this collection.

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